AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and...

19
European Physical Society more than ideas A EUROPEAN SPECIFICATION FOR PHYSICS BACHELOR STUDIES EPS Publications

Transcript of AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and...

Page 1: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

European Physical Societymore than ideas

A EUROPEANSPECIFICATION FOR

PHYSICS BACHELOR STUDIES

EPS Publications

A EUROPEANSPECIFICATION FOR

PHYSICS BACHELOR STUDIES

Submitted to the European Physical Society by

Prof Dr Hendrik FerdinandeUGent- Proeuinstraat 86BE-9000 Gent Belgium

hendrikferdinandeugentbe

EPS Publications

PHYSICS BACHELOR STUDIES

02 EPS PUBLICATIONS 2009

KeywordsBologna Process

European Higher EducationArea (EHEA)European SpecificationPhysics bachelor degree

is study was carried out in 200809Results were published in July 2009

Copyright copy 2009 by the European Physical SocietyAll rights reservedis information may befreely used and copied for non-commercial purposes provided that acknowledgment is given to European

specification for physics bachelor studies and to the copyright of the European Physical Society

For ordering information please contact infoepsorg or write toEuropean Physical Society6 rue des Fregraveres Lumiegravere

FR-68200 Mulhouse FranceTel +33 389 32 94 40Fax +33 389 32 94 49Webwwwepsorg

A free electronic version of this report is available through wwwepsorg

is project has been funded with support from the Lifelong Learning Programme of theEducation and Culture DG of the European Commission (RefAssoc-Educ-SAOG2-12)is publication reflects the views of the authors and the Commission cannot be heldresponsible for any use which may be made of the information contained therein

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 03

02 Keywords03 Table of contents04 Preface05 1 - Introduction

2 - Programme structure amp delivery08 3 - Physics09 4 - Physics bachelor discipline competences10 5 - Physics bachelor generic competences11 References12 Annexes

1 - Membership of the bachelor specification groupAcknowledgements

2 - European Benchmark for Physics Bachelor DegreeSummary1 - Introduction

13 2 - Rationale3 - Overall structure

14 4 - Detailed structure15 5 - Implementation

References

CO

NTEN

TS

A EUROPEAN SPECIFICATIONFOR PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

e European Physical Society (EPS) is a Europe-wide professional association with 41 nationalmember societiese EPS supports the BolognaProcess and provides with a series of specifications ameans to describe the characteristics of the physicsstudy programmes in a European dimensionisseries covers (a) the bachelor or first-cycle or EQFlevel 6 (b) master or second-cycle or EQF level 7 and(c) doctorate or third-cycle level or EQF level 8which together constitute one of the three priorities ofthe Bologna Process [EC09a]e specifications alsodescribe general expectations about the standards forthe award of qualifications at the given level and arti-culate the attributes and capabilities - ie the learningoutcomes - that those possessing such qualificationsshould be able to demonstrateese qualifications arein agreement with the EuropeanQualifications Frame-work (EQF) [EC09b] National statements andguidelines [MS04KF05 IM07LM07 andQA08] havealready been established in some countries and havebeen very influential in designing these specificationse European bachelor level or EQF level 6 corres-ponds to the UNESCO level ISCED 5A [UN06]

is present EPS specification refers to the physicsbachelor degree in a European perspective Specifica-tions are used for a variety of purposes Primarilythey are an important external source of reference forhigher education institutions (HEIs) when new pro-grammes are being designed and developedeyprovide general guidance for articulating the learningoutcomes associated with the programme but are notdetailed descriptions of a core or model curriculumSpecifications provide for variety and flexibility in thedesign of programmes and encourage innovationwithin an agreed overall national regional or institu-tional framework

Specifications also provide support to institutions inpursuit of internal quality assuranceey enable thelearning outcomes specified for a particular pro-gramme to be reviewed and evaluated against agreedgeneral expectations

Finally specifications are among a variety of externalreference points that may be drawn upon for thepurpose of external review Reviewers should not usespecifications as a crude checklist for these purposeshowever Rather they should consider them inconjunction with the relevant programme descrip-tions the institutionsrsquo own internal evaluationdocumentation in order to arrive at a rounded judg-ment based on a broad range of evidence

is present physics bachelor specification has beenundertaken by a European group of physics highereducation specialists (see Annex 1)e groupswork has been funded with support from the Euro-pean Commission [EC07] and was facilitated by theEuropean Physical Societywhich publishes and distri-butes these documentse present document wentthrough a full consultation and validation processwith the wider European academic community andthe stakeholder groups

In due course the specification will be revised toreflect developments in physics (and astronomy) andthe experiences of institutions and others who areworking with ite EPS will initiate revision and willmake arrangements for any necessary modificationsto the document in collaboration with the Europeanphysics community

A Glossary of key terms in higher education can befound in [EU09a] amp [Vl07]

In Annex 2 a common European Benchmark frame-work for Bachelor degrees in Physics is addedIt was kindly provided by the Working Group 1 inthe STEPS (Stakeholders Tune European Physics Stu-dies) TWO network It is aimed at the level of anindicative listing which broadly specifies the com-mon programme which can be found in mostphysics degrees across Europe Also this documentwent through a full consultation and validation pro-cess with the wider European academic communityand the stakeholder groups

04 EPS PUBLICATIONS 2009

PREFACE

PHYSICS BACHELOR STUDIES

1 - Introduction

11 The present specification for physics bachelorprogrammes characterises a European-wide view ofthe competences and achievements that graduatesof physics bachelor degrees should have acquiredthrough their studies and training There exists awide range of programmes delivering such degreesreflecting the varying aspects of physics and diffe-rent national perspectives traditions andeducational policy imperatives However there iswide agreement across Europe of what constitutesthe basics of physics and the essentials of whatshould be included in a first degree in physics Thisspecification relates to the physics components ofprogrammes delivering degrees where physics(including astronomy) and mathematics repre-sents a significant proportion - at least 70 - ofthe programme In a large number of Europeancountries bachelor degrees are a fairly recent deve-lopment inspired by the Bologna Process Physicsdepartments and national physical societies mightwelcome some guidance on what such degreesshould try to achieve and the topics they shouldaim to cover This document builds on extensivework carried out over recent years by the physicsgroup in the TUNING project [TU09a] and over alonger period by the EUPEN group of physicsdepartments [Fe05] both of which have done agreat deal to establish European-wide consensuson the essentials of physics degree programmesWhile this work has been vital in order to establisha European wide consensus several parts of thepresent text rely very much on the Physics Bench-mark produced by the QAA in the UK [QA08]from which they have been directly taken

12 Physics is a major discipline in the EuropeanHigher Education Area (EHEA) with over 100 000full-time equivalent students registered on undergra-duate HE programmes Physics graduates play amajor role in the EU economy However physics is

not only a discipline which is required for scientificand technical professionals it is also an essential partof our understanding of all aspects of nature and theprinciples andmethods which allow us to understandthe universe As such it has wide and deep culturaldimensions and its study is of universal value Itforms the foundation of many of the sciences andtheir applications Physics is also an important back-bone for new advances in technology whichconstitutes an important factor in the developmentand economy of our society

13 Physics is a maturing and demanding disciplineAn understanding of the frontiers of physics oenrequires advanced knowledge which cannot necessa-rily be acquired during a bachelor degree programmee present specification has taken this into accountin interpreting the generic competences of the quali-fication framework for bachelor or first-cycle levelphysics degree programmes

14 Physics degrees will continue to evolve in res-ponse to developments in the discipline and changesin the (secondary) school curriculum Hence thepresent specification concentrates on general lear-ning outcomes and does not specify a model or a corephysics curriculum

2 - Programme structure and delivery

21 Physics is a hierarchical discipline that requires sys-tematic exposure and ordered as well as structuredacquisition of knowledge It is a subject which relies onexperiment and observation as the source of ourknowledge of the physical universe but which com-plements this with theoretical constructs based on afairly small number of all embracing principles andlaws oen expressed and developed using mathema-tics Practical skills have to be developed as also does anappreciation of the link between theory and experiment

EPS PUBLICATIONS 2009 05

PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

lsquois leads to teaching methods that may typicallyinclude [QA08]

bull lectures supported by problem classes and grouptutorial workbull laboratory workbull the use of textbooks and other self-study materialsbull open-ended project work some of which may beteam-basedbull activities devoted to physics-specific and genericcompetence developmentrsquo

In the TUNING methodology [TU09a] the use oflearning outcomes and competences is necessary inorder to make study programmes and their courseunits or modules student-centred and output-oriented This approach requires that the keyknowledge and skills that a student needs to achieveduring the learning process determine the contentof the study programme Modularisation of thestudy programmes is explained in [We09Ke09]Thebalance between the above teaching methods mayvary between institutions programmes andmodules and will evolve with time due to advancesin information technology and pedagogical thinking[Fe05 Ke09]

22 lsquoApproaches to skills development should encom-pass both physics-specific and generic competences[TU09b] developed within the physics contextDevelopment between levels of study should be evi-dent for example laboratory work may becomeopen-ended with more demanding reporting criteriaat the higher levelsComputer skills should include thebasics of programming Acquiring familiarity withprograms for simulation computer algebra and dataanalysis has gained increasing relevance for the physi-cist Skills may also be developed in the use ofcomputers for the control of experiments and theacquisition of datarsquo

23 lsquoA variety of assessment methods are appropriatewithin a physics programme some of which are moresuitable for formative assessment Evidence of the

standards achieved could be obtained from some orall of the following [QA08]

bull time-constrained examinationsbull closed-book and open-book testsbull problem based assignmentsbull laboratory reportsbull observation of practical skillsbull individual project reports (including placement orcase-study reports)bull team project reportsbull oral andor poster presentations including seminarpresentationbull oral examinations amp viva voce interviewsbull essaysbull project outcomes such as computer programs orelectronic circuitsbull electronic mediabull peer and self assessmentrsquo

24 lsquoExamination and test questions should be gra-ded to assess a students understanding of conceptsand ability to develop apply and test mathematicalmodels to perform calculations to solve new pro-blems to communicate physical arguments and toassess critically results in their context Time-constrained work has its place in testing thestudents capacity to organise work as well as tothink and to communicate under pressure Suchassessments should be augmented by others such aspresentations and project reports which allow stu-dents to demonstrate what they can achieve underless severe time constraints Skills such as project-planning and execution research competencesapplication of IT and report writing are best asses-sed in this wayrsquo [QA08]

25 In 2004 the Joint Quality Initiative [JQ04] develo-ped the following descriptors known as the DublinDescriptors (based on Bloomrsquos [Bl56] Taxonomy) todetermine when students in their learning processwould have attained the bachelor levelldquoQualifications that signify completion of the firstcycle are awarded to students who

06 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

bull have demonstrated knowledge and understan-ding in a field of study that builds upon theirgeneral secondary education and is typically at alevel that whilst supported by advanced text-books includes some aspects that wil l beinformed by knowledge of the forefront of theirfield of studybull can apply their knowledge and understanding in amanner that indicates a professional approach totheir work or vocation and have competences typi-cally demonstrated through devising and sustainingarguments and solving problems within their fieldof studybull have the ability to gather and interpret relevant data(usually within their field of study) to inform judg-ments that include reflection on relevant socialscientific or ethical issuesbull can communicate information ideas problems andsolutions to both specialist and non-specialistaudiencesbull have developed those learning skills that are neces-sary for them to continue to undertake further studywith a high degree of autonomyrdquo

In their 2007 London Summit the lsquoBolognarsquoministersinsisted on the use of learning outcomes in curricu-lum design and student-centred pedagogy (see also[TU09a])

26 Institutions which apply the European CreditTransfer and Accumulation System (ECTS)[EC09c] publish their course catalogues on theweb including detailed descriptions of study pro-grammes units of learning university regulationsand student services [Ke09] Course descriptionscontain learning outcomes (what students areexpected to know understand and be able to do)and workload (the time students typically need toachieve the learning outcomes) expressed interms of credits In most cases student workloadranges from 1500 to 1800 hours for an academicyear of 60 ECTS and one credit corresponds to25-30 hours of work Credit transfer and accumu-lation are helped by the use of the ECTS keydocuments (course catalogue learning agreement

and transcript of records) as well as the DiplomaSupplement [DS09]

27 In a recent study [Ke09] it was concluded that thevast majority (almost 90) of the 155 investigatedphysics bachelor programmes from 24 countries havea duration of three years or 180 ECTS credits Only inexceptional cases [eg Ph09] is the duration twoyears Four-year bachelor programmes (240 ECTS)can be found in Greece Ireland Spain LithuaniaMacedonia and Scotland

28 Physics bachelor degree programmes addressthe more general and fundamental topics of phy-sics provide a selection of more advanced topicsand encourage the development of investigativeexperimental mathematical computationalmodelling and other generic competences Thevarious programmes will emphasise differentareas Engineering physics courses might empha-sise experimentation and provide a focus to thecurriculum that is more geared towards industrialapplications

29 Bachelor physics curricula need to cater both forstudents planning to move on to research in indus-try or academia (if the student choose for 70+ ofphysics and mathematics modules) - and obtain asubsequent physics master degree andor a docto-rate degree - as well as for students looking for abroad physics-based education which will providethem with a firm base of generic skills and makethem eminently employable The latter kinds ofcurricula have a long tradition in the UK and Ire-land while in almost all continental countries suchprogrammes are rather new and will require bothemployers and graduates to develop a better unders-tanding of the careers and job opportunities theyprovide A recent inquiry [Eu09b] by the Eurydicenetwork of the EC concludes lsquoWhatever their prac-tice all countries face serious challenges in adaptingto fast-changing societal demands and ensuring thatqualifications ndash in particular those of the first cycle ndashgive access to the labour marketrsquo

EPS PUBLICATIONS 2009 07

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 2: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

A EUROPEANSPECIFICATION FOR

PHYSICS BACHELOR STUDIES

Submitted to the European Physical Society by

Prof Dr Hendrik FerdinandeUGent- Proeuinstraat 86BE-9000 Gent Belgium

hendrikferdinandeugentbe

EPS Publications

PHYSICS BACHELOR STUDIES

02 EPS PUBLICATIONS 2009

KeywordsBologna Process

European Higher EducationArea (EHEA)European SpecificationPhysics bachelor degree

is study was carried out in 200809Results were published in July 2009

Copyright copy 2009 by the European Physical SocietyAll rights reservedis information may befreely used and copied for non-commercial purposes provided that acknowledgment is given to European

specification for physics bachelor studies and to the copyright of the European Physical Society

For ordering information please contact infoepsorg or write toEuropean Physical Society6 rue des Fregraveres Lumiegravere

FR-68200 Mulhouse FranceTel +33 389 32 94 40Fax +33 389 32 94 49Webwwwepsorg

A free electronic version of this report is available through wwwepsorg

is project has been funded with support from the Lifelong Learning Programme of theEducation and Culture DG of the European Commission (RefAssoc-Educ-SAOG2-12)is publication reflects the views of the authors and the Commission cannot be heldresponsible for any use which may be made of the information contained therein

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 03

02 Keywords03 Table of contents04 Preface05 1 - Introduction

2 - Programme structure amp delivery08 3 - Physics09 4 - Physics bachelor discipline competences10 5 - Physics bachelor generic competences11 References12 Annexes

1 - Membership of the bachelor specification groupAcknowledgements

2 - European Benchmark for Physics Bachelor DegreeSummary1 - Introduction

13 2 - Rationale3 - Overall structure

14 4 - Detailed structure15 5 - Implementation

References

CO

NTEN

TS

A EUROPEAN SPECIFICATIONFOR PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

e European Physical Society (EPS) is a Europe-wide professional association with 41 nationalmember societiese EPS supports the BolognaProcess and provides with a series of specifications ameans to describe the characteristics of the physicsstudy programmes in a European dimensionisseries covers (a) the bachelor or first-cycle or EQFlevel 6 (b) master or second-cycle or EQF level 7 and(c) doctorate or third-cycle level or EQF level 8which together constitute one of the three priorities ofthe Bologna Process [EC09a]e specifications alsodescribe general expectations about the standards forthe award of qualifications at the given level and arti-culate the attributes and capabilities - ie the learningoutcomes - that those possessing such qualificationsshould be able to demonstrateese qualifications arein agreement with the EuropeanQualifications Frame-work (EQF) [EC09b] National statements andguidelines [MS04KF05 IM07LM07 andQA08] havealready been established in some countries and havebeen very influential in designing these specificationse European bachelor level or EQF level 6 corres-ponds to the UNESCO level ISCED 5A [UN06]

is present EPS specification refers to the physicsbachelor degree in a European perspective Specifica-tions are used for a variety of purposes Primarilythey are an important external source of reference forhigher education institutions (HEIs) when new pro-grammes are being designed and developedeyprovide general guidance for articulating the learningoutcomes associated with the programme but are notdetailed descriptions of a core or model curriculumSpecifications provide for variety and flexibility in thedesign of programmes and encourage innovationwithin an agreed overall national regional or institu-tional framework

Specifications also provide support to institutions inpursuit of internal quality assuranceey enable thelearning outcomes specified for a particular pro-gramme to be reviewed and evaluated against agreedgeneral expectations

Finally specifications are among a variety of externalreference points that may be drawn upon for thepurpose of external review Reviewers should not usespecifications as a crude checklist for these purposeshowever Rather they should consider them inconjunction with the relevant programme descrip-tions the institutionsrsquo own internal evaluationdocumentation in order to arrive at a rounded judg-ment based on a broad range of evidence

is present physics bachelor specification has beenundertaken by a European group of physics highereducation specialists (see Annex 1)e groupswork has been funded with support from the Euro-pean Commission [EC07] and was facilitated by theEuropean Physical Societywhich publishes and distri-butes these documentse present document wentthrough a full consultation and validation processwith the wider European academic community andthe stakeholder groups

In due course the specification will be revised toreflect developments in physics (and astronomy) andthe experiences of institutions and others who areworking with ite EPS will initiate revision and willmake arrangements for any necessary modificationsto the document in collaboration with the Europeanphysics community

A Glossary of key terms in higher education can befound in [EU09a] amp [Vl07]

In Annex 2 a common European Benchmark frame-work for Bachelor degrees in Physics is addedIt was kindly provided by the Working Group 1 inthe STEPS (Stakeholders Tune European Physics Stu-dies) TWO network It is aimed at the level of anindicative listing which broadly specifies the com-mon programme which can be found in mostphysics degrees across Europe Also this documentwent through a full consultation and validation pro-cess with the wider European academic communityand the stakeholder groups

04 EPS PUBLICATIONS 2009

PREFACE

PHYSICS BACHELOR STUDIES

1 - Introduction

11 The present specification for physics bachelorprogrammes characterises a European-wide view ofthe competences and achievements that graduatesof physics bachelor degrees should have acquiredthrough their studies and training There exists awide range of programmes delivering such degreesreflecting the varying aspects of physics and diffe-rent national perspectives traditions andeducational policy imperatives However there iswide agreement across Europe of what constitutesthe basics of physics and the essentials of whatshould be included in a first degree in physics Thisspecification relates to the physics components ofprogrammes delivering degrees where physics(including astronomy) and mathematics repre-sents a significant proportion - at least 70 - ofthe programme In a large number of Europeancountries bachelor degrees are a fairly recent deve-lopment inspired by the Bologna Process Physicsdepartments and national physical societies mightwelcome some guidance on what such degreesshould try to achieve and the topics they shouldaim to cover This document builds on extensivework carried out over recent years by the physicsgroup in the TUNING project [TU09a] and over alonger period by the EUPEN group of physicsdepartments [Fe05] both of which have done agreat deal to establish European-wide consensuson the essentials of physics degree programmesWhile this work has been vital in order to establisha European wide consensus several parts of thepresent text rely very much on the Physics Bench-mark produced by the QAA in the UK [QA08]from which they have been directly taken

12 Physics is a major discipline in the EuropeanHigher Education Area (EHEA) with over 100 000full-time equivalent students registered on undergra-duate HE programmes Physics graduates play amajor role in the EU economy However physics is

not only a discipline which is required for scientificand technical professionals it is also an essential partof our understanding of all aspects of nature and theprinciples andmethods which allow us to understandthe universe As such it has wide and deep culturaldimensions and its study is of universal value Itforms the foundation of many of the sciences andtheir applications Physics is also an important back-bone for new advances in technology whichconstitutes an important factor in the developmentand economy of our society

13 Physics is a maturing and demanding disciplineAn understanding of the frontiers of physics oenrequires advanced knowledge which cannot necessa-rily be acquired during a bachelor degree programmee present specification has taken this into accountin interpreting the generic competences of the quali-fication framework for bachelor or first-cycle levelphysics degree programmes

14 Physics degrees will continue to evolve in res-ponse to developments in the discipline and changesin the (secondary) school curriculum Hence thepresent specification concentrates on general lear-ning outcomes and does not specify a model or a corephysics curriculum

2 - Programme structure and delivery

21 Physics is a hierarchical discipline that requires sys-tematic exposure and ordered as well as structuredacquisition of knowledge It is a subject which relies onexperiment and observation as the source of ourknowledge of the physical universe but which com-plements this with theoretical constructs based on afairly small number of all embracing principles andlaws oen expressed and developed using mathema-tics Practical skills have to be developed as also does anappreciation of the link between theory and experiment

EPS PUBLICATIONS 2009 05

PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

lsquois leads to teaching methods that may typicallyinclude [QA08]

bull lectures supported by problem classes and grouptutorial workbull laboratory workbull the use of textbooks and other self-study materialsbull open-ended project work some of which may beteam-basedbull activities devoted to physics-specific and genericcompetence developmentrsquo

In the TUNING methodology [TU09a] the use oflearning outcomes and competences is necessary inorder to make study programmes and their courseunits or modules student-centred and output-oriented This approach requires that the keyknowledge and skills that a student needs to achieveduring the learning process determine the contentof the study programme Modularisation of thestudy programmes is explained in [We09Ke09]Thebalance between the above teaching methods mayvary between institutions programmes andmodules and will evolve with time due to advancesin information technology and pedagogical thinking[Fe05 Ke09]

22 lsquoApproaches to skills development should encom-pass both physics-specific and generic competences[TU09b] developed within the physics contextDevelopment between levels of study should be evi-dent for example laboratory work may becomeopen-ended with more demanding reporting criteriaat the higher levelsComputer skills should include thebasics of programming Acquiring familiarity withprograms for simulation computer algebra and dataanalysis has gained increasing relevance for the physi-cist Skills may also be developed in the use ofcomputers for the control of experiments and theacquisition of datarsquo

23 lsquoA variety of assessment methods are appropriatewithin a physics programme some of which are moresuitable for formative assessment Evidence of the

standards achieved could be obtained from some orall of the following [QA08]

bull time-constrained examinationsbull closed-book and open-book testsbull problem based assignmentsbull laboratory reportsbull observation of practical skillsbull individual project reports (including placement orcase-study reports)bull team project reportsbull oral andor poster presentations including seminarpresentationbull oral examinations amp viva voce interviewsbull essaysbull project outcomes such as computer programs orelectronic circuitsbull electronic mediabull peer and self assessmentrsquo

24 lsquoExamination and test questions should be gra-ded to assess a students understanding of conceptsand ability to develop apply and test mathematicalmodels to perform calculations to solve new pro-blems to communicate physical arguments and toassess critically results in their context Time-constrained work has its place in testing thestudents capacity to organise work as well as tothink and to communicate under pressure Suchassessments should be augmented by others such aspresentations and project reports which allow stu-dents to demonstrate what they can achieve underless severe time constraints Skills such as project-planning and execution research competencesapplication of IT and report writing are best asses-sed in this wayrsquo [QA08]

25 In 2004 the Joint Quality Initiative [JQ04] develo-ped the following descriptors known as the DublinDescriptors (based on Bloomrsquos [Bl56] Taxonomy) todetermine when students in their learning processwould have attained the bachelor levelldquoQualifications that signify completion of the firstcycle are awarded to students who

06 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

bull have demonstrated knowledge and understan-ding in a field of study that builds upon theirgeneral secondary education and is typically at alevel that whilst supported by advanced text-books includes some aspects that wil l beinformed by knowledge of the forefront of theirfield of studybull can apply their knowledge and understanding in amanner that indicates a professional approach totheir work or vocation and have competences typi-cally demonstrated through devising and sustainingarguments and solving problems within their fieldof studybull have the ability to gather and interpret relevant data(usually within their field of study) to inform judg-ments that include reflection on relevant socialscientific or ethical issuesbull can communicate information ideas problems andsolutions to both specialist and non-specialistaudiencesbull have developed those learning skills that are neces-sary for them to continue to undertake further studywith a high degree of autonomyrdquo

In their 2007 London Summit the lsquoBolognarsquoministersinsisted on the use of learning outcomes in curricu-lum design and student-centred pedagogy (see also[TU09a])

26 Institutions which apply the European CreditTransfer and Accumulation System (ECTS)[EC09c] publish their course catalogues on theweb including detailed descriptions of study pro-grammes units of learning university regulationsand student services [Ke09] Course descriptionscontain learning outcomes (what students areexpected to know understand and be able to do)and workload (the time students typically need toachieve the learning outcomes) expressed interms of credits In most cases student workloadranges from 1500 to 1800 hours for an academicyear of 60 ECTS and one credit corresponds to25-30 hours of work Credit transfer and accumu-lation are helped by the use of the ECTS keydocuments (course catalogue learning agreement

and transcript of records) as well as the DiplomaSupplement [DS09]

27 In a recent study [Ke09] it was concluded that thevast majority (almost 90) of the 155 investigatedphysics bachelor programmes from 24 countries havea duration of three years or 180 ECTS credits Only inexceptional cases [eg Ph09] is the duration twoyears Four-year bachelor programmes (240 ECTS)can be found in Greece Ireland Spain LithuaniaMacedonia and Scotland

28 Physics bachelor degree programmes addressthe more general and fundamental topics of phy-sics provide a selection of more advanced topicsand encourage the development of investigativeexperimental mathematical computationalmodelling and other generic competences Thevarious programmes will emphasise differentareas Engineering physics courses might empha-sise experimentation and provide a focus to thecurriculum that is more geared towards industrialapplications

29 Bachelor physics curricula need to cater both forstudents planning to move on to research in indus-try or academia (if the student choose for 70+ ofphysics and mathematics modules) - and obtain asubsequent physics master degree andor a docto-rate degree - as well as for students looking for abroad physics-based education which will providethem with a firm base of generic skills and makethem eminently employable The latter kinds ofcurricula have a long tradition in the UK and Ire-land while in almost all continental countries suchprogrammes are rather new and will require bothemployers and graduates to develop a better unders-tanding of the careers and job opportunities theyprovide A recent inquiry [Eu09b] by the Eurydicenetwork of the EC concludes lsquoWhatever their prac-tice all countries face serious challenges in adaptingto fast-changing societal demands and ensuring thatqualifications ndash in particular those of the first cycle ndashgive access to the labour marketrsquo

EPS PUBLICATIONS 2009 07

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 3: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

02 EPS PUBLICATIONS 2009

KeywordsBologna Process

European Higher EducationArea (EHEA)European SpecificationPhysics bachelor degree

is study was carried out in 200809Results were published in July 2009

Copyright copy 2009 by the European Physical SocietyAll rights reservedis information may befreely used and copied for non-commercial purposes provided that acknowledgment is given to European

specification for physics bachelor studies and to the copyright of the European Physical Society

For ordering information please contact infoepsorg or write toEuropean Physical Society6 rue des Fregraveres Lumiegravere

FR-68200 Mulhouse FranceTel +33 389 32 94 40Fax +33 389 32 94 49Webwwwepsorg

A free electronic version of this report is available through wwwepsorg

is project has been funded with support from the Lifelong Learning Programme of theEducation and Culture DG of the European Commission (RefAssoc-Educ-SAOG2-12)is publication reflects the views of the authors and the Commission cannot be heldresponsible for any use which may be made of the information contained therein

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 03

02 Keywords03 Table of contents04 Preface05 1 - Introduction

2 - Programme structure amp delivery08 3 - Physics09 4 - Physics bachelor discipline competences10 5 - Physics bachelor generic competences11 References12 Annexes

1 - Membership of the bachelor specification groupAcknowledgements

2 - European Benchmark for Physics Bachelor DegreeSummary1 - Introduction

13 2 - Rationale3 - Overall structure

14 4 - Detailed structure15 5 - Implementation

References

CO

NTEN

TS

A EUROPEAN SPECIFICATIONFOR PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

e European Physical Society (EPS) is a Europe-wide professional association with 41 nationalmember societiese EPS supports the BolognaProcess and provides with a series of specifications ameans to describe the characteristics of the physicsstudy programmes in a European dimensionisseries covers (a) the bachelor or first-cycle or EQFlevel 6 (b) master or second-cycle or EQF level 7 and(c) doctorate or third-cycle level or EQF level 8which together constitute one of the three priorities ofthe Bologna Process [EC09a]e specifications alsodescribe general expectations about the standards forthe award of qualifications at the given level and arti-culate the attributes and capabilities - ie the learningoutcomes - that those possessing such qualificationsshould be able to demonstrateese qualifications arein agreement with the EuropeanQualifications Frame-work (EQF) [EC09b] National statements andguidelines [MS04KF05 IM07LM07 andQA08] havealready been established in some countries and havebeen very influential in designing these specificationse European bachelor level or EQF level 6 corres-ponds to the UNESCO level ISCED 5A [UN06]

is present EPS specification refers to the physicsbachelor degree in a European perspective Specifica-tions are used for a variety of purposes Primarilythey are an important external source of reference forhigher education institutions (HEIs) when new pro-grammes are being designed and developedeyprovide general guidance for articulating the learningoutcomes associated with the programme but are notdetailed descriptions of a core or model curriculumSpecifications provide for variety and flexibility in thedesign of programmes and encourage innovationwithin an agreed overall national regional or institu-tional framework

Specifications also provide support to institutions inpursuit of internal quality assuranceey enable thelearning outcomes specified for a particular pro-gramme to be reviewed and evaluated against agreedgeneral expectations

Finally specifications are among a variety of externalreference points that may be drawn upon for thepurpose of external review Reviewers should not usespecifications as a crude checklist for these purposeshowever Rather they should consider them inconjunction with the relevant programme descrip-tions the institutionsrsquo own internal evaluationdocumentation in order to arrive at a rounded judg-ment based on a broad range of evidence

is present physics bachelor specification has beenundertaken by a European group of physics highereducation specialists (see Annex 1)e groupswork has been funded with support from the Euro-pean Commission [EC07] and was facilitated by theEuropean Physical Societywhich publishes and distri-butes these documentse present document wentthrough a full consultation and validation processwith the wider European academic community andthe stakeholder groups

In due course the specification will be revised toreflect developments in physics (and astronomy) andthe experiences of institutions and others who areworking with ite EPS will initiate revision and willmake arrangements for any necessary modificationsto the document in collaboration with the Europeanphysics community

A Glossary of key terms in higher education can befound in [EU09a] amp [Vl07]

In Annex 2 a common European Benchmark frame-work for Bachelor degrees in Physics is addedIt was kindly provided by the Working Group 1 inthe STEPS (Stakeholders Tune European Physics Stu-dies) TWO network It is aimed at the level of anindicative listing which broadly specifies the com-mon programme which can be found in mostphysics degrees across Europe Also this documentwent through a full consultation and validation pro-cess with the wider European academic communityand the stakeholder groups

04 EPS PUBLICATIONS 2009

PREFACE

PHYSICS BACHELOR STUDIES

1 - Introduction

11 The present specification for physics bachelorprogrammes characterises a European-wide view ofthe competences and achievements that graduatesof physics bachelor degrees should have acquiredthrough their studies and training There exists awide range of programmes delivering such degreesreflecting the varying aspects of physics and diffe-rent national perspectives traditions andeducational policy imperatives However there iswide agreement across Europe of what constitutesthe basics of physics and the essentials of whatshould be included in a first degree in physics Thisspecification relates to the physics components ofprogrammes delivering degrees where physics(including astronomy) and mathematics repre-sents a significant proportion - at least 70 - ofthe programme In a large number of Europeancountries bachelor degrees are a fairly recent deve-lopment inspired by the Bologna Process Physicsdepartments and national physical societies mightwelcome some guidance on what such degreesshould try to achieve and the topics they shouldaim to cover This document builds on extensivework carried out over recent years by the physicsgroup in the TUNING project [TU09a] and over alonger period by the EUPEN group of physicsdepartments [Fe05] both of which have done agreat deal to establish European-wide consensuson the essentials of physics degree programmesWhile this work has been vital in order to establisha European wide consensus several parts of thepresent text rely very much on the Physics Bench-mark produced by the QAA in the UK [QA08]from which they have been directly taken

12 Physics is a major discipline in the EuropeanHigher Education Area (EHEA) with over 100 000full-time equivalent students registered on undergra-duate HE programmes Physics graduates play amajor role in the EU economy However physics is

not only a discipline which is required for scientificand technical professionals it is also an essential partof our understanding of all aspects of nature and theprinciples andmethods which allow us to understandthe universe As such it has wide and deep culturaldimensions and its study is of universal value Itforms the foundation of many of the sciences andtheir applications Physics is also an important back-bone for new advances in technology whichconstitutes an important factor in the developmentand economy of our society

13 Physics is a maturing and demanding disciplineAn understanding of the frontiers of physics oenrequires advanced knowledge which cannot necessa-rily be acquired during a bachelor degree programmee present specification has taken this into accountin interpreting the generic competences of the quali-fication framework for bachelor or first-cycle levelphysics degree programmes

14 Physics degrees will continue to evolve in res-ponse to developments in the discipline and changesin the (secondary) school curriculum Hence thepresent specification concentrates on general lear-ning outcomes and does not specify a model or a corephysics curriculum

2 - Programme structure and delivery

21 Physics is a hierarchical discipline that requires sys-tematic exposure and ordered as well as structuredacquisition of knowledge It is a subject which relies onexperiment and observation as the source of ourknowledge of the physical universe but which com-plements this with theoretical constructs based on afairly small number of all embracing principles andlaws oen expressed and developed using mathema-tics Practical skills have to be developed as also does anappreciation of the link between theory and experiment

EPS PUBLICATIONS 2009 05

PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

lsquois leads to teaching methods that may typicallyinclude [QA08]

bull lectures supported by problem classes and grouptutorial workbull laboratory workbull the use of textbooks and other self-study materialsbull open-ended project work some of which may beteam-basedbull activities devoted to physics-specific and genericcompetence developmentrsquo

In the TUNING methodology [TU09a] the use oflearning outcomes and competences is necessary inorder to make study programmes and their courseunits or modules student-centred and output-oriented This approach requires that the keyknowledge and skills that a student needs to achieveduring the learning process determine the contentof the study programme Modularisation of thestudy programmes is explained in [We09Ke09]Thebalance between the above teaching methods mayvary between institutions programmes andmodules and will evolve with time due to advancesin information technology and pedagogical thinking[Fe05 Ke09]

22 lsquoApproaches to skills development should encom-pass both physics-specific and generic competences[TU09b] developed within the physics contextDevelopment between levels of study should be evi-dent for example laboratory work may becomeopen-ended with more demanding reporting criteriaat the higher levelsComputer skills should include thebasics of programming Acquiring familiarity withprograms for simulation computer algebra and dataanalysis has gained increasing relevance for the physi-cist Skills may also be developed in the use ofcomputers for the control of experiments and theacquisition of datarsquo

23 lsquoA variety of assessment methods are appropriatewithin a physics programme some of which are moresuitable for formative assessment Evidence of the

standards achieved could be obtained from some orall of the following [QA08]

bull time-constrained examinationsbull closed-book and open-book testsbull problem based assignmentsbull laboratory reportsbull observation of practical skillsbull individual project reports (including placement orcase-study reports)bull team project reportsbull oral andor poster presentations including seminarpresentationbull oral examinations amp viva voce interviewsbull essaysbull project outcomes such as computer programs orelectronic circuitsbull electronic mediabull peer and self assessmentrsquo

24 lsquoExamination and test questions should be gra-ded to assess a students understanding of conceptsand ability to develop apply and test mathematicalmodels to perform calculations to solve new pro-blems to communicate physical arguments and toassess critically results in their context Time-constrained work has its place in testing thestudents capacity to organise work as well as tothink and to communicate under pressure Suchassessments should be augmented by others such aspresentations and project reports which allow stu-dents to demonstrate what they can achieve underless severe time constraints Skills such as project-planning and execution research competencesapplication of IT and report writing are best asses-sed in this wayrsquo [QA08]

25 In 2004 the Joint Quality Initiative [JQ04] develo-ped the following descriptors known as the DublinDescriptors (based on Bloomrsquos [Bl56] Taxonomy) todetermine when students in their learning processwould have attained the bachelor levelldquoQualifications that signify completion of the firstcycle are awarded to students who

06 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

bull have demonstrated knowledge and understan-ding in a field of study that builds upon theirgeneral secondary education and is typically at alevel that whilst supported by advanced text-books includes some aspects that wil l beinformed by knowledge of the forefront of theirfield of studybull can apply their knowledge and understanding in amanner that indicates a professional approach totheir work or vocation and have competences typi-cally demonstrated through devising and sustainingarguments and solving problems within their fieldof studybull have the ability to gather and interpret relevant data(usually within their field of study) to inform judg-ments that include reflection on relevant socialscientific or ethical issuesbull can communicate information ideas problems andsolutions to both specialist and non-specialistaudiencesbull have developed those learning skills that are neces-sary for them to continue to undertake further studywith a high degree of autonomyrdquo

In their 2007 London Summit the lsquoBolognarsquoministersinsisted on the use of learning outcomes in curricu-lum design and student-centred pedagogy (see also[TU09a])

26 Institutions which apply the European CreditTransfer and Accumulation System (ECTS)[EC09c] publish their course catalogues on theweb including detailed descriptions of study pro-grammes units of learning university regulationsand student services [Ke09] Course descriptionscontain learning outcomes (what students areexpected to know understand and be able to do)and workload (the time students typically need toachieve the learning outcomes) expressed interms of credits In most cases student workloadranges from 1500 to 1800 hours for an academicyear of 60 ECTS and one credit corresponds to25-30 hours of work Credit transfer and accumu-lation are helped by the use of the ECTS keydocuments (course catalogue learning agreement

and transcript of records) as well as the DiplomaSupplement [DS09]

27 In a recent study [Ke09] it was concluded that thevast majority (almost 90) of the 155 investigatedphysics bachelor programmes from 24 countries havea duration of three years or 180 ECTS credits Only inexceptional cases [eg Ph09] is the duration twoyears Four-year bachelor programmes (240 ECTS)can be found in Greece Ireland Spain LithuaniaMacedonia and Scotland

28 Physics bachelor degree programmes addressthe more general and fundamental topics of phy-sics provide a selection of more advanced topicsand encourage the development of investigativeexperimental mathematical computationalmodelling and other generic competences Thevarious programmes will emphasise differentareas Engineering physics courses might empha-sise experimentation and provide a focus to thecurriculum that is more geared towards industrialapplications

29 Bachelor physics curricula need to cater both forstudents planning to move on to research in indus-try or academia (if the student choose for 70+ ofphysics and mathematics modules) - and obtain asubsequent physics master degree andor a docto-rate degree - as well as for students looking for abroad physics-based education which will providethem with a firm base of generic skills and makethem eminently employable The latter kinds ofcurricula have a long tradition in the UK and Ire-land while in almost all continental countries suchprogrammes are rather new and will require bothemployers and graduates to develop a better unders-tanding of the careers and job opportunities theyprovide A recent inquiry [Eu09b] by the Eurydicenetwork of the EC concludes lsquoWhatever their prac-tice all countries face serious challenges in adaptingto fast-changing societal demands and ensuring thatqualifications ndash in particular those of the first cycle ndashgive access to the labour marketrsquo

EPS PUBLICATIONS 2009 07

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 4: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 03

02 Keywords03 Table of contents04 Preface05 1 - Introduction

2 - Programme structure amp delivery08 3 - Physics09 4 - Physics bachelor discipline competences10 5 - Physics bachelor generic competences11 References12 Annexes

1 - Membership of the bachelor specification groupAcknowledgements

2 - European Benchmark for Physics Bachelor DegreeSummary1 - Introduction

13 2 - Rationale3 - Overall structure

14 4 - Detailed structure15 5 - Implementation

References

CO

NTEN

TS

A EUROPEAN SPECIFICATIONFOR PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

e European Physical Society (EPS) is a Europe-wide professional association with 41 nationalmember societiese EPS supports the BolognaProcess and provides with a series of specifications ameans to describe the characteristics of the physicsstudy programmes in a European dimensionisseries covers (a) the bachelor or first-cycle or EQFlevel 6 (b) master or second-cycle or EQF level 7 and(c) doctorate or third-cycle level or EQF level 8which together constitute one of the three priorities ofthe Bologna Process [EC09a]e specifications alsodescribe general expectations about the standards forthe award of qualifications at the given level and arti-culate the attributes and capabilities - ie the learningoutcomes - that those possessing such qualificationsshould be able to demonstrateese qualifications arein agreement with the EuropeanQualifications Frame-work (EQF) [EC09b] National statements andguidelines [MS04KF05 IM07LM07 andQA08] havealready been established in some countries and havebeen very influential in designing these specificationse European bachelor level or EQF level 6 corres-ponds to the UNESCO level ISCED 5A [UN06]

is present EPS specification refers to the physicsbachelor degree in a European perspective Specifica-tions are used for a variety of purposes Primarilythey are an important external source of reference forhigher education institutions (HEIs) when new pro-grammes are being designed and developedeyprovide general guidance for articulating the learningoutcomes associated with the programme but are notdetailed descriptions of a core or model curriculumSpecifications provide for variety and flexibility in thedesign of programmes and encourage innovationwithin an agreed overall national regional or institu-tional framework

Specifications also provide support to institutions inpursuit of internal quality assuranceey enable thelearning outcomes specified for a particular pro-gramme to be reviewed and evaluated against agreedgeneral expectations

Finally specifications are among a variety of externalreference points that may be drawn upon for thepurpose of external review Reviewers should not usespecifications as a crude checklist for these purposeshowever Rather they should consider them inconjunction with the relevant programme descrip-tions the institutionsrsquo own internal evaluationdocumentation in order to arrive at a rounded judg-ment based on a broad range of evidence

is present physics bachelor specification has beenundertaken by a European group of physics highereducation specialists (see Annex 1)e groupswork has been funded with support from the Euro-pean Commission [EC07] and was facilitated by theEuropean Physical Societywhich publishes and distri-butes these documentse present document wentthrough a full consultation and validation processwith the wider European academic community andthe stakeholder groups

In due course the specification will be revised toreflect developments in physics (and astronomy) andthe experiences of institutions and others who areworking with ite EPS will initiate revision and willmake arrangements for any necessary modificationsto the document in collaboration with the Europeanphysics community

A Glossary of key terms in higher education can befound in [EU09a] amp [Vl07]

In Annex 2 a common European Benchmark frame-work for Bachelor degrees in Physics is addedIt was kindly provided by the Working Group 1 inthe STEPS (Stakeholders Tune European Physics Stu-dies) TWO network It is aimed at the level of anindicative listing which broadly specifies the com-mon programme which can be found in mostphysics degrees across Europe Also this documentwent through a full consultation and validation pro-cess with the wider European academic communityand the stakeholder groups

04 EPS PUBLICATIONS 2009

PREFACE

PHYSICS BACHELOR STUDIES

1 - Introduction

11 The present specification for physics bachelorprogrammes characterises a European-wide view ofthe competences and achievements that graduatesof physics bachelor degrees should have acquiredthrough their studies and training There exists awide range of programmes delivering such degreesreflecting the varying aspects of physics and diffe-rent national perspectives traditions andeducational policy imperatives However there iswide agreement across Europe of what constitutesthe basics of physics and the essentials of whatshould be included in a first degree in physics Thisspecification relates to the physics components ofprogrammes delivering degrees where physics(including astronomy) and mathematics repre-sents a significant proportion - at least 70 - ofthe programme In a large number of Europeancountries bachelor degrees are a fairly recent deve-lopment inspired by the Bologna Process Physicsdepartments and national physical societies mightwelcome some guidance on what such degreesshould try to achieve and the topics they shouldaim to cover This document builds on extensivework carried out over recent years by the physicsgroup in the TUNING project [TU09a] and over alonger period by the EUPEN group of physicsdepartments [Fe05] both of which have done agreat deal to establish European-wide consensuson the essentials of physics degree programmesWhile this work has been vital in order to establisha European wide consensus several parts of thepresent text rely very much on the Physics Bench-mark produced by the QAA in the UK [QA08]from which they have been directly taken

12 Physics is a major discipline in the EuropeanHigher Education Area (EHEA) with over 100 000full-time equivalent students registered on undergra-duate HE programmes Physics graduates play amajor role in the EU economy However physics is

not only a discipline which is required for scientificand technical professionals it is also an essential partof our understanding of all aspects of nature and theprinciples andmethods which allow us to understandthe universe As such it has wide and deep culturaldimensions and its study is of universal value Itforms the foundation of many of the sciences andtheir applications Physics is also an important back-bone for new advances in technology whichconstitutes an important factor in the developmentand economy of our society

13 Physics is a maturing and demanding disciplineAn understanding of the frontiers of physics oenrequires advanced knowledge which cannot necessa-rily be acquired during a bachelor degree programmee present specification has taken this into accountin interpreting the generic competences of the quali-fication framework for bachelor or first-cycle levelphysics degree programmes

14 Physics degrees will continue to evolve in res-ponse to developments in the discipline and changesin the (secondary) school curriculum Hence thepresent specification concentrates on general lear-ning outcomes and does not specify a model or a corephysics curriculum

2 - Programme structure and delivery

21 Physics is a hierarchical discipline that requires sys-tematic exposure and ordered as well as structuredacquisition of knowledge It is a subject which relies onexperiment and observation as the source of ourknowledge of the physical universe but which com-plements this with theoretical constructs based on afairly small number of all embracing principles andlaws oen expressed and developed using mathema-tics Practical skills have to be developed as also does anappreciation of the link between theory and experiment

EPS PUBLICATIONS 2009 05

PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

lsquois leads to teaching methods that may typicallyinclude [QA08]

bull lectures supported by problem classes and grouptutorial workbull laboratory workbull the use of textbooks and other self-study materialsbull open-ended project work some of which may beteam-basedbull activities devoted to physics-specific and genericcompetence developmentrsquo

In the TUNING methodology [TU09a] the use oflearning outcomes and competences is necessary inorder to make study programmes and their courseunits or modules student-centred and output-oriented This approach requires that the keyknowledge and skills that a student needs to achieveduring the learning process determine the contentof the study programme Modularisation of thestudy programmes is explained in [We09Ke09]Thebalance between the above teaching methods mayvary between institutions programmes andmodules and will evolve with time due to advancesin information technology and pedagogical thinking[Fe05 Ke09]

22 lsquoApproaches to skills development should encom-pass both physics-specific and generic competences[TU09b] developed within the physics contextDevelopment between levels of study should be evi-dent for example laboratory work may becomeopen-ended with more demanding reporting criteriaat the higher levelsComputer skills should include thebasics of programming Acquiring familiarity withprograms for simulation computer algebra and dataanalysis has gained increasing relevance for the physi-cist Skills may also be developed in the use ofcomputers for the control of experiments and theacquisition of datarsquo

23 lsquoA variety of assessment methods are appropriatewithin a physics programme some of which are moresuitable for formative assessment Evidence of the

standards achieved could be obtained from some orall of the following [QA08]

bull time-constrained examinationsbull closed-book and open-book testsbull problem based assignmentsbull laboratory reportsbull observation of practical skillsbull individual project reports (including placement orcase-study reports)bull team project reportsbull oral andor poster presentations including seminarpresentationbull oral examinations amp viva voce interviewsbull essaysbull project outcomes such as computer programs orelectronic circuitsbull electronic mediabull peer and self assessmentrsquo

24 lsquoExamination and test questions should be gra-ded to assess a students understanding of conceptsand ability to develop apply and test mathematicalmodels to perform calculations to solve new pro-blems to communicate physical arguments and toassess critically results in their context Time-constrained work has its place in testing thestudents capacity to organise work as well as tothink and to communicate under pressure Suchassessments should be augmented by others such aspresentations and project reports which allow stu-dents to demonstrate what they can achieve underless severe time constraints Skills such as project-planning and execution research competencesapplication of IT and report writing are best asses-sed in this wayrsquo [QA08]

25 In 2004 the Joint Quality Initiative [JQ04] develo-ped the following descriptors known as the DublinDescriptors (based on Bloomrsquos [Bl56] Taxonomy) todetermine when students in their learning processwould have attained the bachelor levelldquoQualifications that signify completion of the firstcycle are awarded to students who

06 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

bull have demonstrated knowledge and understan-ding in a field of study that builds upon theirgeneral secondary education and is typically at alevel that whilst supported by advanced text-books includes some aspects that wil l beinformed by knowledge of the forefront of theirfield of studybull can apply their knowledge and understanding in amanner that indicates a professional approach totheir work or vocation and have competences typi-cally demonstrated through devising and sustainingarguments and solving problems within their fieldof studybull have the ability to gather and interpret relevant data(usually within their field of study) to inform judg-ments that include reflection on relevant socialscientific or ethical issuesbull can communicate information ideas problems andsolutions to both specialist and non-specialistaudiencesbull have developed those learning skills that are neces-sary for them to continue to undertake further studywith a high degree of autonomyrdquo

In their 2007 London Summit the lsquoBolognarsquoministersinsisted on the use of learning outcomes in curricu-lum design and student-centred pedagogy (see also[TU09a])

26 Institutions which apply the European CreditTransfer and Accumulation System (ECTS)[EC09c] publish their course catalogues on theweb including detailed descriptions of study pro-grammes units of learning university regulationsand student services [Ke09] Course descriptionscontain learning outcomes (what students areexpected to know understand and be able to do)and workload (the time students typically need toachieve the learning outcomes) expressed interms of credits In most cases student workloadranges from 1500 to 1800 hours for an academicyear of 60 ECTS and one credit corresponds to25-30 hours of work Credit transfer and accumu-lation are helped by the use of the ECTS keydocuments (course catalogue learning agreement

and transcript of records) as well as the DiplomaSupplement [DS09]

27 In a recent study [Ke09] it was concluded that thevast majority (almost 90) of the 155 investigatedphysics bachelor programmes from 24 countries havea duration of three years or 180 ECTS credits Only inexceptional cases [eg Ph09] is the duration twoyears Four-year bachelor programmes (240 ECTS)can be found in Greece Ireland Spain LithuaniaMacedonia and Scotland

28 Physics bachelor degree programmes addressthe more general and fundamental topics of phy-sics provide a selection of more advanced topicsand encourage the development of investigativeexperimental mathematical computationalmodelling and other generic competences Thevarious programmes will emphasise differentareas Engineering physics courses might empha-sise experimentation and provide a focus to thecurriculum that is more geared towards industrialapplications

29 Bachelor physics curricula need to cater both forstudents planning to move on to research in indus-try or academia (if the student choose for 70+ ofphysics and mathematics modules) - and obtain asubsequent physics master degree andor a docto-rate degree - as well as for students looking for abroad physics-based education which will providethem with a firm base of generic skills and makethem eminently employable The latter kinds ofcurricula have a long tradition in the UK and Ire-land while in almost all continental countries suchprogrammes are rather new and will require bothemployers and graduates to develop a better unders-tanding of the careers and job opportunities theyprovide A recent inquiry [Eu09b] by the Eurydicenetwork of the EC concludes lsquoWhatever their prac-tice all countries face serious challenges in adaptingto fast-changing societal demands and ensuring thatqualifications ndash in particular those of the first cycle ndashgive access to the labour marketrsquo

EPS PUBLICATIONS 2009 07

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 5: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

e European Physical Society (EPS) is a Europe-wide professional association with 41 nationalmember societiese EPS supports the BolognaProcess and provides with a series of specifications ameans to describe the characteristics of the physicsstudy programmes in a European dimensionisseries covers (a) the bachelor or first-cycle or EQFlevel 6 (b) master or second-cycle or EQF level 7 and(c) doctorate or third-cycle level or EQF level 8which together constitute one of the three priorities ofthe Bologna Process [EC09a]e specifications alsodescribe general expectations about the standards forthe award of qualifications at the given level and arti-culate the attributes and capabilities - ie the learningoutcomes - that those possessing such qualificationsshould be able to demonstrateese qualifications arein agreement with the EuropeanQualifications Frame-work (EQF) [EC09b] National statements andguidelines [MS04KF05 IM07LM07 andQA08] havealready been established in some countries and havebeen very influential in designing these specificationse European bachelor level or EQF level 6 corres-ponds to the UNESCO level ISCED 5A [UN06]

is present EPS specification refers to the physicsbachelor degree in a European perspective Specifica-tions are used for a variety of purposes Primarilythey are an important external source of reference forhigher education institutions (HEIs) when new pro-grammes are being designed and developedeyprovide general guidance for articulating the learningoutcomes associated with the programme but are notdetailed descriptions of a core or model curriculumSpecifications provide for variety and flexibility in thedesign of programmes and encourage innovationwithin an agreed overall national regional or institu-tional framework

Specifications also provide support to institutions inpursuit of internal quality assuranceey enable thelearning outcomes specified for a particular pro-gramme to be reviewed and evaluated against agreedgeneral expectations

Finally specifications are among a variety of externalreference points that may be drawn upon for thepurpose of external review Reviewers should not usespecifications as a crude checklist for these purposeshowever Rather they should consider them inconjunction with the relevant programme descrip-tions the institutionsrsquo own internal evaluationdocumentation in order to arrive at a rounded judg-ment based on a broad range of evidence

is present physics bachelor specification has beenundertaken by a European group of physics highereducation specialists (see Annex 1)e groupswork has been funded with support from the Euro-pean Commission [EC07] and was facilitated by theEuropean Physical Societywhich publishes and distri-butes these documentse present document wentthrough a full consultation and validation processwith the wider European academic community andthe stakeholder groups

In due course the specification will be revised toreflect developments in physics (and astronomy) andthe experiences of institutions and others who areworking with ite EPS will initiate revision and willmake arrangements for any necessary modificationsto the document in collaboration with the Europeanphysics community

A Glossary of key terms in higher education can befound in [EU09a] amp [Vl07]

In Annex 2 a common European Benchmark frame-work for Bachelor degrees in Physics is addedIt was kindly provided by the Working Group 1 inthe STEPS (Stakeholders Tune European Physics Stu-dies) TWO network It is aimed at the level of anindicative listing which broadly specifies the com-mon programme which can be found in mostphysics degrees across Europe Also this documentwent through a full consultation and validation pro-cess with the wider European academic communityand the stakeholder groups

04 EPS PUBLICATIONS 2009

PREFACE

PHYSICS BACHELOR STUDIES

1 - Introduction

11 The present specification for physics bachelorprogrammes characterises a European-wide view ofthe competences and achievements that graduatesof physics bachelor degrees should have acquiredthrough their studies and training There exists awide range of programmes delivering such degreesreflecting the varying aspects of physics and diffe-rent national perspectives traditions andeducational policy imperatives However there iswide agreement across Europe of what constitutesthe basics of physics and the essentials of whatshould be included in a first degree in physics Thisspecification relates to the physics components ofprogrammes delivering degrees where physics(including astronomy) and mathematics repre-sents a significant proportion - at least 70 - ofthe programme In a large number of Europeancountries bachelor degrees are a fairly recent deve-lopment inspired by the Bologna Process Physicsdepartments and national physical societies mightwelcome some guidance on what such degreesshould try to achieve and the topics they shouldaim to cover This document builds on extensivework carried out over recent years by the physicsgroup in the TUNING project [TU09a] and over alonger period by the EUPEN group of physicsdepartments [Fe05] both of which have done agreat deal to establish European-wide consensuson the essentials of physics degree programmesWhile this work has been vital in order to establisha European wide consensus several parts of thepresent text rely very much on the Physics Bench-mark produced by the QAA in the UK [QA08]from which they have been directly taken

12 Physics is a major discipline in the EuropeanHigher Education Area (EHEA) with over 100 000full-time equivalent students registered on undergra-duate HE programmes Physics graduates play amajor role in the EU economy However physics is

not only a discipline which is required for scientificand technical professionals it is also an essential partof our understanding of all aspects of nature and theprinciples andmethods which allow us to understandthe universe As such it has wide and deep culturaldimensions and its study is of universal value Itforms the foundation of many of the sciences andtheir applications Physics is also an important back-bone for new advances in technology whichconstitutes an important factor in the developmentand economy of our society

13 Physics is a maturing and demanding disciplineAn understanding of the frontiers of physics oenrequires advanced knowledge which cannot necessa-rily be acquired during a bachelor degree programmee present specification has taken this into accountin interpreting the generic competences of the quali-fication framework for bachelor or first-cycle levelphysics degree programmes

14 Physics degrees will continue to evolve in res-ponse to developments in the discipline and changesin the (secondary) school curriculum Hence thepresent specification concentrates on general lear-ning outcomes and does not specify a model or a corephysics curriculum

2 - Programme structure and delivery

21 Physics is a hierarchical discipline that requires sys-tematic exposure and ordered as well as structuredacquisition of knowledge It is a subject which relies onexperiment and observation as the source of ourknowledge of the physical universe but which com-plements this with theoretical constructs based on afairly small number of all embracing principles andlaws oen expressed and developed using mathema-tics Practical skills have to be developed as also does anappreciation of the link between theory and experiment

EPS PUBLICATIONS 2009 05

PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

lsquois leads to teaching methods that may typicallyinclude [QA08]

bull lectures supported by problem classes and grouptutorial workbull laboratory workbull the use of textbooks and other self-study materialsbull open-ended project work some of which may beteam-basedbull activities devoted to physics-specific and genericcompetence developmentrsquo

In the TUNING methodology [TU09a] the use oflearning outcomes and competences is necessary inorder to make study programmes and their courseunits or modules student-centred and output-oriented This approach requires that the keyknowledge and skills that a student needs to achieveduring the learning process determine the contentof the study programme Modularisation of thestudy programmes is explained in [We09Ke09]Thebalance between the above teaching methods mayvary between institutions programmes andmodules and will evolve with time due to advancesin information technology and pedagogical thinking[Fe05 Ke09]

22 lsquoApproaches to skills development should encom-pass both physics-specific and generic competences[TU09b] developed within the physics contextDevelopment between levels of study should be evi-dent for example laboratory work may becomeopen-ended with more demanding reporting criteriaat the higher levelsComputer skills should include thebasics of programming Acquiring familiarity withprograms for simulation computer algebra and dataanalysis has gained increasing relevance for the physi-cist Skills may also be developed in the use ofcomputers for the control of experiments and theacquisition of datarsquo

23 lsquoA variety of assessment methods are appropriatewithin a physics programme some of which are moresuitable for formative assessment Evidence of the

standards achieved could be obtained from some orall of the following [QA08]

bull time-constrained examinationsbull closed-book and open-book testsbull problem based assignmentsbull laboratory reportsbull observation of practical skillsbull individual project reports (including placement orcase-study reports)bull team project reportsbull oral andor poster presentations including seminarpresentationbull oral examinations amp viva voce interviewsbull essaysbull project outcomes such as computer programs orelectronic circuitsbull electronic mediabull peer and self assessmentrsquo

24 lsquoExamination and test questions should be gra-ded to assess a students understanding of conceptsand ability to develop apply and test mathematicalmodels to perform calculations to solve new pro-blems to communicate physical arguments and toassess critically results in their context Time-constrained work has its place in testing thestudents capacity to organise work as well as tothink and to communicate under pressure Suchassessments should be augmented by others such aspresentations and project reports which allow stu-dents to demonstrate what they can achieve underless severe time constraints Skills such as project-planning and execution research competencesapplication of IT and report writing are best asses-sed in this wayrsquo [QA08]

25 In 2004 the Joint Quality Initiative [JQ04] develo-ped the following descriptors known as the DublinDescriptors (based on Bloomrsquos [Bl56] Taxonomy) todetermine when students in their learning processwould have attained the bachelor levelldquoQualifications that signify completion of the firstcycle are awarded to students who

06 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

bull have demonstrated knowledge and understan-ding in a field of study that builds upon theirgeneral secondary education and is typically at alevel that whilst supported by advanced text-books includes some aspects that wil l beinformed by knowledge of the forefront of theirfield of studybull can apply their knowledge and understanding in amanner that indicates a professional approach totheir work or vocation and have competences typi-cally demonstrated through devising and sustainingarguments and solving problems within their fieldof studybull have the ability to gather and interpret relevant data(usually within their field of study) to inform judg-ments that include reflection on relevant socialscientific or ethical issuesbull can communicate information ideas problems andsolutions to both specialist and non-specialistaudiencesbull have developed those learning skills that are neces-sary for them to continue to undertake further studywith a high degree of autonomyrdquo

In their 2007 London Summit the lsquoBolognarsquoministersinsisted on the use of learning outcomes in curricu-lum design and student-centred pedagogy (see also[TU09a])

26 Institutions which apply the European CreditTransfer and Accumulation System (ECTS)[EC09c] publish their course catalogues on theweb including detailed descriptions of study pro-grammes units of learning university regulationsand student services [Ke09] Course descriptionscontain learning outcomes (what students areexpected to know understand and be able to do)and workload (the time students typically need toachieve the learning outcomes) expressed interms of credits In most cases student workloadranges from 1500 to 1800 hours for an academicyear of 60 ECTS and one credit corresponds to25-30 hours of work Credit transfer and accumu-lation are helped by the use of the ECTS keydocuments (course catalogue learning agreement

and transcript of records) as well as the DiplomaSupplement [DS09]

27 In a recent study [Ke09] it was concluded that thevast majority (almost 90) of the 155 investigatedphysics bachelor programmes from 24 countries havea duration of three years or 180 ECTS credits Only inexceptional cases [eg Ph09] is the duration twoyears Four-year bachelor programmes (240 ECTS)can be found in Greece Ireland Spain LithuaniaMacedonia and Scotland

28 Physics bachelor degree programmes addressthe more general and fundamental topics of phy-sics provide a selection of more advanced topicsand encourage the development of investigativeexperimental mathematical computationalmodelling and other generic competences Thevarious programmes will emphasise differentareas Engineering physics courses might empha-sise experimentation and provide a focus to thecurriculum that is more geared towards industrialapplications

29 Bachelor physics curricula need to cater both forstudents planning to move on to research in indus-try or academia (if the student choose for 70+ ofphysics and mathematics modules) - and obtain asubsequent physics master degree andor a docto-rate degree - as well as for students looking for abroad physics-based education which will providethem with a firm base of generic skills and makethem eminently employable The latter kinds ofcurricula have a long tradition in the UK and Ire-land while in almost all continental countries suchprogrammes are rather new and will require bothemployers and graduates to develop a better unders-tanding of the careers and job opportunities theyprovide A recent inquiry [Eu09b] by the Eurydicenetwork of the EC concludes lsquoWhatever their prac-tice all countries face serious challenges in adaptingto fast-changing societal demands and ensuring thatqualifications ndash in particular those of the first cycle ndashgive access to the labour marketrsquo

EPS PUBLICATIONS 2009 07

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 6: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

1 - Introduction

11 The present specification for physics bachelorprogrammes characterises a European-wide view ofthe competences and achievements that graduatesof physics bachelor degrees should have acquiredthrough their studies and training There exists awide range of programmes delivering such degreesreflecting the varying aspects of physics and diffe-rent national perspectives traditions andeducational policy imperatives However there iswide agreement across Europe of what constitutesthe basics of physics and the essentials of whatshould be included in a first degree in physics Thisspecification relates to the physics components ofprogrammes delivering degrees where physics(including astronomy) and mathematics repre-sents a significant proportion - at least 70 - ofthe programme In a large number of Europeancountries bachelor degrees are a fairly recent deve-lopment inspired by the Bologna Process Physicsdepartments and national physical societies mightwelcome some guidance on what such degreesshould try to achieve and the topics they shouldaim to cover This document builds on extensivework carried out over recent years by the physicsgroup in the TUNING project [TU09a] and over alonger period by the EUPEN group of physicsdepartments [Fe05] both of which have done agreat deal to establish European-wide consensuson the essentials of physics degree programmesWhile this work has been vital in order to establisha European wide consensus several parts of thepresent text rely very much on the Physics Bench-mark produced by the QAA in the UK [QA08]from which they have been directly taken

12 Physics is a major discipline in the EuropeanHigher Education Area (EHEA) with over 100 000full-time equivalent students registered on undergra-duate HE programmes Physics graduates play amajor role in the EU economy However physics is

not only a discipline which is required for scientificand technical professionals it is also an essential partof our understanding of all aspects of nature and theprinciples andmethods which allow us to understandthe universe As such it has wide and deep culturaldimensions and its study is of universal value Itforms the foundation of many of the sciences andtheir applications Physics is also an important back-bone for new advances in technology whichconstitutes an important factor in the developmentand economy of our society

13 Physics is a maturing and demanding disciplineAn understanding of the frontiers of physics oenrequires advanced knowledge which cannot necessa-rily be acquired during a bachelor degree programmee present specification has taken this into accountin interpreting the generic competences of the quali-fication framework for bachelor or first-cycle levelphysics degree programmes

14 Physics degrees will continue to evolve in res-ponse to developments in the discipline and changesin the (secondary) school curriculum Hence thepresent specification concentrates on general lear-ning outcomes and does not specify a model or a corephysics curriculum

2 - Programme structure and delivery

21 Physics is a hierarchical discipline that requires sys-tematic exposure and ordered as well as structuredacquisition of knowledge It is a subject which relies onexperiment and observation as the source of ourknowledge of the physical universe but which com-plements this with theoretical constructs based on afairly small number of all embracing principles andlaws oen expressed and developed using mathema-tics Practical skills have to be developed as also does anappreciation of the link between theory and experiment

EPS PUBLICATIONS 2009 05

PHYSICS BACHELOR STUDIES

PHYSICS BACHELOR STUDIES

lsquois leads to teaching methods that may typicallyinclude [QA08]

bull lectures supported by problem classes and grouptutorial workbull laboratory workbull the use of textbooks and other self-study materialsbull open-ended project work some of which may beteam-basedbull activities devoted to physics-specific and genericcompetence developmentrsquo

In the TUNING methodology [TU09a] the use oflearning outcomes and competences is necessary inorder to make study programmes and their courseunits or modules student-centred and output-oriented This approach requires that the keyknowledge and skills that a student needs to achieveduring the learning process determine the contentof the study programme Modularisation of thestudy programmes is explained in [We09Ke09]Thebalance between the above teaching methods mayvary between institutions programmes andmodules and will evolve with time due to advancesin information technology and pedagogical thinking[Fe05 Ke09]

22 lsquoApproaches to skills development should encom-pass both physics-specific and generic competences[TU09b] developed within the physics contextDevelopment between levels of study should be evi-dent for example laboratory work may becomeopen-ended with more demanding reporting criteriaat the higher levelsComputer skills should include thebasics of programming Acquiring familiarity withprograms for simulation computer algebra and dataanalysis has gained increasing relevance for the physi-cist Skills may also be developed in the use ofcomputers for the control of experiments and theacquisition of datarsquo

23 lsquoA variety of assessment methods are appropriatewithin a physics programme some of which are moresuitable for formative assessment Evidence of the

standards achieved could be obtained from some orall of the following [QA08]

bull time-constrained examinationsbull closed-book and open-book testsbull problem based assignmentsbull laboratory reportsbull observation of practical skillsbull individual project reports (including placement orcase-study reports)bull team project reportsbull oral andor poster presentations including seminarpresentationbull oral examinations amp viva voce interviewsbull essaysbull project outcomes such as computer programs orelectronic circuitsbull electronic mediabull peer and self assessmentrsquo

24 lsquoExamination and test questions should be gra-ded to assess a students understanding of conceptsand ability to develop apply and test mathematicalmodels to perform calculations to solve new pro-blems to communicate physical arguments and toassess critically results in their context Time-constrained work has its place in testing thestudents capacity to organise work as well as tothink and to communicate under pressure Suchassessments should be augmented by others such aspresentations and project reports which allow stu-dents to demonstrate what they can achieve underless severe time constraints Skills such as project-planning and execution research competencesapplication of IT and report writing are best asses-sed in this wayrsquo [QA08]

25 In 2004 the Joint Quality Initiative [JQ04] develo-ped the following descriptors known as the DublinDescriptors (based on Bloomrsquos [Bl56] Taxonomy) todetermine when students in their learning processwould have attained the bachelor levelldquoQualifications that signify completion of the firstcycle are awarded to students who

06 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

bull have demonstrated knowledge and understan-ding in a field of study that builds upon theirgeneral secondary education and is typically at alevel that whilst supported by advanced text-books includes some aspects that wil l beinformed by knowledge of the forefront of theirfield of studybull can apply their knowledge and understanding in amanner that indicates a professional approach totheir work or vocation and have competences typi-cally demonstrated through devising and sustainingarguments and solving problems within their fieldof studybull have the ability to gather and interpret relevant data(usually within their field of study) to inform judg-ments that include reflection on relevant socialscientific or ethical issuesbull can communicate information ideas problems andsolutions to both specialist and non-specialistaudiencesbull have developed those learning skills that are neces-sary for them to continue to undertake further studywith a high degree of autonomyrdquo

In their 2007 London Summit the lsquoBolognarsquoministersinsisted on the use of learning outcomes in curricu-lum design and student-centred pedagogy (see also[TU09a])

26 Institutions which apply the European CreditTransfer and Accumulation System (ECTS)[EC09c] publish their course catalogues on theweb including detailed descriptions of study pro-grammes units of learning university regulationsand student services [Ke09] Course descriptionscontain learning outcomes (what students areexpected to know understand and be able to do)and workload (the time students typically need toachieve the learning outcomes) expressed interms of credits In most cases student workloadranges from 1500 to 1800 hours for an academicyear of 60 ECTS and one credit corresponds to25-30 hours of work Credit transfer and accumu-lation are helped by the use of the ECTS keydocuments (course catalogue learning agreement

and transcript of records) as well as the DiplomaSupplement [DS09]

27 In a recent study [Ke09] it was concluded that thevast majority (almost 90) of the 155 investigatedphysics bachelor programmes from 24 countries havea duration of three years or 180 ECTS credits Only inexceptional cases [eg Ph09] is the duration twoyears Four-year bachelor programmes (240 ECTS)can be found in Greece Ireland Spain LithuaniaMacedonia and Scotland

28 Physics bachelor degree programmes addressthe more general and fundamental topics of phy-sics provide a selection of more advanced topicsand encourage the development of investigativeexperimental mathematical computationalmodelling and other generic competences Thevarious programmes will emphasise differentareas Engineering physics courses might empha-sise experimentation and provide a focus to thecurriculum that is more geared towards industrialapplications

29 Bachelor physics curricula need to cater both forstudents planning to move on to research in indus-try or academia (if the student choose for 70+ ofphysics and mathematics modules) - and obtain asubsequent physics master degree andor a docto-rate degree - as well as for students looking for abroad physics-based education which will providethem with a firm base of generic skills and makethem eminently employable The latter kinds ofcurricula have a long tradition in the UK and Ire-land while in almost all continental countries suchprogrammes are rather new and will require bothemployers and graduates to develop a better unders-tanding of the careers and job opportunities theyprovide A recent inquiry [Eu09b] by the Eurydicenetwork of the EC concludes lsquoWhatever their prac-tice all countries face serious challenges in adaptingto fast-changing societal demands and ensuring thatqualifications ndash in particular those of the first cycle ndashgive access to the labour marketrsquo

EPS PUBLICATIONS 2009 07

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 7: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

lsquois leads to teaching methods that may typicallyinclude [QA08]

bull lectures supported by problem classes and grouptutorial workbull laboratory workbull the use of textbooks and other self-study materialsbull open-ended project work some of which may beteam-basedbull activities devoted to physics-specific and genericcompetence developmentrsquo

In the TUNING methodology [TU09a] the use oflearning outcomes and competences is necessary inorder to make study programmes and their courseunits or modules student-centred and output-oriented This approach requires that the keyknowledge and skills that a student needs to achieveduring the learning process determine the contentof the study programme Modularisation of thestudy programmes is explained in [We09Ke09]Thebalance between the above teaching methods mayvary between institutions programmes andmodules and will evolve with time due to advancesin information technology and pedagogical thinking[Fe05 Ke09]

22 lsquoApproaches to skills development should encom-pass both physics-specific and generic competences[TU09b] developed within the physics contextDevelopment between levels of study should be evi-dent for example laboratory work may becomeopen-ended with more demanding reporting criteriaat the higher levelsComputer skills should include thebasics of programming Acquiring familiarity withprograms for simulation computer algebra and dataanalysis has gained increasing relevance for the physi-cist Skills may also be developed in the use ofcomputers for the control of experiments and theacquisition of datarsquo

23 lsquoA variety of assessment methods are appropriatewithin a physics programme some of which are moresuitable for formative assessment Evidence of the

standards achieved could be obtained from some orall of the following [QA08]

bull time-constrained examinationsbull closed-book and open-book testsbull problem based assignmentsbull laboratory reportsbull observation of practical skillsbull individual project reports (including placement orcase-study reports)bull team project reportsbull oral andor poster presentations including seminarpresentationbull oral examinations amp viva voce interviewsbull essaysbull project outcomes such as computer programs orelectronic circuitsbull electronic mediabull peer and self assessmentrsquo

24 lsquoExamination and test questions should be gra-ded to assess a students understanding of conceptsand ability to develop apply and test mathematicalmodels to perform calculations to solve new pro-blems to communicate physical arguments and toassess critically results in their context Time-constrained work has its place in testing thestudents capacity to organise work as well as tothink and to communicate under pressure Suchassessments should be augmented by others such aspresentations and project reports which allow stu-dents to demonstrate what they can achieve underless severe time constraints Skills such as project-planning and execution research competencesapplication of IT and report writing are best asses-sed in this wayrsquo [QA08]

25 In 2004 the Joint Quality Initiative [JQ04] develo-ped the following descriptors known as the DublinDescriptors (based on Bloomrsquos [Bl56] Taxonomy) todetermine when students in their learning processwould have attained the bachelor levelldquoQualifications that signify completion of the firstcycle are awarded to students who

06 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

bull have demonstrated knowledge and understan-ding in a field of study that builds upon theirgeneral secondary education and is typically at alevel that whilst supported by advanced text-books includes some aspects that wil l beinformed by knowledge of the forefront of theirfield of studybull can apply their knowledge and understanding in amanner that indicates a professional approach totheir work or vocation and have competences typi-cally demonstrated through devising and sustainingarguments and solving problems within their fieldof studybull have the ability to gather and interpret relevant data(usually within their field of study) to inform judg-ments that include reflection on relevant socialscientific or ethical issuesbull can communicate information ideas problems andsolutions to both specialist and non-specialistaudiencesbull have developed those learning skills that are neces-sary for them to continue to undertake further studywith a high degree of autonomyrdquo

In their 2007 London Summit the lsquoBolognarsquoministersinsisted on the use of learning outcomes in curricu-lum design and student-centred pedagogy (see also[TU09a])

26 Institutions which apply the European CreditTransfer and Accumulation System (ECTS)[EC09c] publish their course catalogues on theweb including detailed descriptions of study pro-grammes units of learning university regulationsand student services [Ke09] Course descriptionscontain learning outcomes (what students areexpected to know understand and be able to do)and workload (the time students typically need toachieve the learning outcomes) expressed interms of credits In most cases student workloadranges from 1500 to 1800 hours for an academicyear of 60 ECTS and one credit corresponds to25-30 hours of work Credit transfer and accumu-lation are helped by the use of the ECTS keydocuments (course catalogue learning agreement

and transcript of records) as well as the DiplomaSupplement [DS09]

27 In a recent study [Ke09] it was concluded that thevast majority (almost 90) of the 155 investigatedphysics bachelor programmes from 24 countries havea duration of three years or 180 ECTS credits Only inexceptional cases [eg Ph09] is the duration twoyears Four-year bachelor programmes (240 ECTS)can be found in Greece Ireland Spain LithuaniaMacedonia and Scotland

28 Physics bachelor degree programmes addressthe more general and fundamental topics of phy-sics provide a selection of more advanced topicsand encourage the development of investigativeexperimental mathematical computationalmodelling and other generic competences Thevarious programmes will emphasise differentareas Engineering physics courses might empha-sise experimentation and provide a focus to thecurriculum that is more geared towards industrialapplications

29 Bachelor physics curricula need to cater both forstudents planning to move on to research in indus-try or academia (if the student choose for 70+ ofphysics and mathematics modules) - and obtain asubsequent physics master degree andor a docto-rate degree - as well as for students looking for abroad physics-based education which will providethem with a firm base of generic skills and makethem eminently employable The latter kinds ofcurricula have a long tradition in the UK and Ire-land while in almost all continental countries suchprogrammes are rather new and will require bothemployers and graduates to develop a better unders-tanding of the careers and job opportunities theyprovide A recent inquiry [Eu09b] by the Eurydicenetwork of the EC concludes lsquoWhatever their prac-tice all countries face serious challenges in adaptingto fast-changing societal demands and ensuring thatqualifications ndash in particular those of the first cycle ndashgive access to the labour marketrsquo

EPS PUBLICATIONS 2009 07

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 8: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

bull have demonstrated knowledge and understan-ding in a field of study that builds upon theirgeneral secondary education and is typically at alevel that whilst supported by advanced text-books includes some aspects that wil l beinformed by knowledge of the forefront of theirfield of studybull can apply their knowledge and understanding in amanner that indicates a professional approach totheir work or vocation and have competences typi-cally demonstrated through devising and sustainingarguments and solving problems within their fieldof studybull have the ability to gather and interpret relevant data(usually within their field of study) to inform judg-ments that include reflection on relevant socialscientific or ethical issuesbull can communicate information ideas problems andsolutions to both specialist and non-specialistaudiencesbull have developed those learning skills that are neces-sary for them to continue to undertake further studywith a high degree of autonomyrdquo

In their 2007 London Summit the lsquoBolognarsquoministersinsisted on the use of learning outcomes in curricu-lum design and student-centred pedagogy (see also[TU09a])

26 Institutions which apply the European CreditTransfer and Accumulation System (ECTS)[EC09c] publish their course catalogues on theweb including detailed descriptions of study pro-grammes units of learning university regulationsand student services [Ke09] Course descriptionscontain learning outcomes (what students areexpected to know understand and be able to do)and workload (the time students typically need toachieve the learning outcomes) expressed interms of credits In most cases student workloadranges from 1500 to 1800 hours for an academicyear of 60 ECTS and one credit corresponds to25-30 hours of work Credit transfer and accumu-lation are helped by the use of the ECTS keydocuments (course catalogue learning agreement

and transcript of records) as well as the DiplomaSupplement [DS09]

27 In a recent study [Ke09] it was concluded that thevast majority (almost 90) of the 155 investigatedphysics bachelor programmes from 24 countries havea duration of three years or 180 ECTS credits Only inexceptional cases [eg Ph09] is the duration twoyears Four-year bachelor programmes (240 ECTS)can be found in Greece Ireland Spain LithuaniaMacedonia and Scotland

28 Physics bachelor degree programmes addressthe more general and fundamental topics of phy-sics provide a selection of more advanced topicsand encourage the development of investigativeexperimental mathematical computationalmodelling and other generic competences Thevarious programmes will emphasise differentareas Engineering physics courses might empha-sise experimentation and provide a focus to thecurriculum that is more geared towards industrialapplications

29 Bachelor physics curricula need to cater both forstudents planning to move on to research in indus-try or academia (if the student choose for 70+ ofphysics and mathematics modules) - and obtain asubsequent physics master degree andor a docto-rate degree - as well as for students looking for abroad physics-based education which will providethem with a firm base of generic skills and makethem eminently employable The latter kinds ofcurricula have a long tradition in the UK and Ire-land while in almost all continental countries suchprogrammes are rather new and will require bothemployers and graduates to develop a better unders-tanding of the careers and job opportunities theyprovide A recent inquiry [Eu09b] by the Eurydicenetwork of the EC concludes lsquoWhatever their prac-tice all countries face serious challenges in adaptingto fast-changing societal demands and ensuring thatqualifications ndash in particular those of the first cycle ndashgive access to the labour marketrsquo

EPS PUBLICATIONS 2009 07

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 9: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

3 - Physics

31 lsquoPhysics is concerned with the quantitative obser-vation understanding and prediction of naturalphenomena and the behaviour of human-made sys-tems It deals with profound questions about thenature of the universe and with some of the mostimportant practical environmental and technologicalissues of our time Its scope is broad and involvesmathematics and theory measurement ie quantita-tive experimentation and observations computingtechnology materials and information theoryConcepts and techniques from physics also drivedevelopments in related disciplines including chemis-try computing engineering materials sciencemathematics medicine and the life sciences meteo-rology and statisticsrsquo [QA08]

32 lsquoPhysics is both an experimental and a theoreti-cal discipline that is continuously evolving It isdeeply rooted in the idea that even complex systemscan be understood by identifying a few key quanti-ties such as energy and momentum and theuniversal principles that govern them Part of theappeal of physics is that there are relatively few suchprinciples and that these apply throughout scienceand not just in physics The laws of mechanics are agood example deduced by Newton after studyingobservations of planetary motion they govern sys-tems familiar from everyday life as well as many ofthe phenomena observed in the movement of starsand galaxiesrsquo [QA08]

33 Physics as an experimental science lsquoe skills andmethods used to make measurements are an integralpart of physicse final test of the validity of anytheory is whether it agrees with experiment Manyimportant discoveries aremade as a result of the deve-lopment of some new experimental technique Forexample techniques developed to liquefy helium sub-sequently led to the totally unexpected discovery ofsuperconductivity superfluidity and the whole fieldof low temperature physics Instruments developedoriginally in physics frequently find applications in

other branches of science for example electromagne-tic radiation emitted by electron accelerators whichwere originally designed to study elementary particlesis now used to study the properties of materials inengineeringbiology andmedicinersquo [QA08]Moreoverdevices such as transistors and lasers which weredeveloped within basic physics research programmeshave revolutionised technology

34 lsquoIn order to make quantitative predictions phy-sics uses mathematical models The types ofapproximation used to find satisfactory models ofexperimental observations turn out to be very simi-lar whether the underlying laws are those ofclassical physics statistical mechanics or quantumtheory Typically an idealised model of some pheno-menon is established the equations describing themodel in mathematical terms are solved (often withfurther approximations) and the results comparedwith experimental observation Sometimes a modelis applicable to very different circumstances Forexample the same statistical model that describesthe behaviour of electrons in metals is equallyapplicable to white dwarf starsrsquo [QA08]

35 lsquoProgress in physics requires imagination andcreativity It is oen the result of collaboration betweenphysicists with dierent backgrounds and increasinglyinvolves exchange of ideas and techniques with peoplefrom other disciplinesWithin physics there are threebroad categories of activity experimental (or observa-tional) computational and theoretical althoughmanyphysicists span these categoriesrsquo [QA08]

36 lsquoStudying physics at a university brings benefitsthat last a lifetime and knowledge and skills that arevaluable outside the field of physics Such benefitsinclude a practical approach to problem solvingoften using mathematical formulation and solutionthe ability to reason clearly and to communicatecomplex ideas IT and self-study skills along withthe pleasure and satisfaction that comes from beingable to understand the latest discoveries in physics

08 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 10: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

or natural scienceAfter graduation physicists workin a wide variety of employment including researchdevelopment and education in industry and acade-mia and increasingly in areas such as business andfinance where they are sought for their analyticaland synthetical approaches to the solution of pro-blemsrsquo [QA08]

4 - Physics bachelor disciplinecompetences

41 Curricula will usually distinguish between funda-mental ideas and the description and modellingof phenomena

e fundamentals which all students need to cover tosome extent include

bull (classical) mechanicsbull electromagnetismbull quantum physicsbull thermodynamicsbull statistical physicsbullwave phenomenabull opticsbull properties of matter their elementary constituentsand interactions

Bachelor students should also familiarise themselvesat the introductory level with the application of thefundamental principles to particular areas

bull atomic physicsbull nuclear and particle physicsbull condensed matter physicsbull physics of materialsbull plasmasbull physics of fluids

In case astrophysics and astronomy courses are part ofthe programme these may include the application ofphysical principles to

bull cosmologybull structure formation and evolutionof stars and galaxies

bull planetary systemsbull high-energy phenomena in the universeIn addition the curricula should help students toachieve some qualitative understanding of currentdevelopments at the frontiers of the physics discipline

42 Students should learn that physics is a quantita-tive field of study and appreciate the use and power ofmathematics formodelling the physical world and sol-ving problems Mathematical competence is anessential part of a physics degree

43 Physics curricula should expose students to theexperience of the practical nature of physics [IU08]They should provide students with the skills neces-sary to plan investigations and collect and analysedata (including estimation of inherent uncertain-ties) These skills may be acquired as part of a coursein a laboratory or by a range of alternatives inclu-ding computer simulations These experimentalcompetences could also be acquired by providingopportunities for student internship in national ormultinational laboratories or industrial research anddevelopment centres Practical work should thus bea vital and challenging part of a physics degree andall undergraduates in physics should have an appre-ciation of natural phenomena in an experimentalcontext Students should also become proficient inpresenting experimental results or theoreticalconclusions and in the writing of scientific reportsIndependent project work should be used to facili-tate the development of students skills in researchand planning (by use of data bases and publishedliterature) and to enhance their ability to assess cri-tically the link between theoretical results andexperimental observation

44 Physics bachelor graduates should be able

bull to formulate and tackle problems in physics Forexample they should be able to identify the appro-priate physical principles to use special and limitingcases and order-of-magnitude estimates to guide

EPS PUBLICATIONS 2009 09

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 11: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

their thinking about a problem and to present asolution by making their assumptions and approxi-mations explicitbull to plan and execute an experiment or investigationand to report the resultsey should be able to useappropriatemethods to analyse their data and to eva-luate the level of uncertaintyey should also beable to relate any conclusions they make to currenttheories of the physics involvedbull to use mathematics to describe the physical worldThey should have an understanding of mathema-tical modelling and the role of approximationThey should be able to compare critically theresults of model calculations with those fromexperiment and observation They should also beable to make error and statistical analysis of expe-rimental data to ensure the validity andsignificance of results

5 - Physics bachelor genericcompetences

A physics bachelor degree should enhance the follo-wing generic competences [TU09b amp Fe05] (most ofthe following text is taken directly from [QA08])

Problem-solving

Physics degree programmes engage students in sol-ving problems with well-defined solutionsey willalso gain experience in tackling open-ended problemsStudents should develop their ability to formulate pro-blems in precise terms and to identify key issuesey should develop confidence in pursuing dierentapproaches in order to make progress on challengingor non-standard problems

Analytical

Physics helps students learn the need to pay attentionto detail and to develop their ability tomanipulate pre-cise and intricate ideas to construct logical argumentsand to use technical language correctly

Investigative

Students will have opportunities to develop theirskills of independent investigation Generally stu-dents will have experience with extractingimportant information from textbooks and otherliterature with searching databases and with inter-acting with colleagues

Communication

Physics and themathematics used in physics deal withsurprising ideas and di$cult concepts good commu-nication is essential A physics degree should developstudents ability to listen carefully to read demandingtexts and to present di$cult ideas and complex infor-mation in a clear and concise manner

Information Technology

During their studies students will develop their com-puting and IT skills in a variety of ways includingtheir ability to use appropriate soware such as pro-gramming languages and soware packages

Personal

Students should develop their ability to work inde-pendently to use their initiative to organise theiractivities tomeet deadlines and to interact constructi-vely with other people

Language

Since a mobile labour force with language compe-tences is crucial for economic growth and betterjobs enabling European enterprises to competeeffectively in the global marketplace multilingua-lism contributes to personal development andreinforces social cohesion Students should at leastdevelop an oral and written knowledge of Englishthe lingua franca of physics

10 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 12: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

Ethical behaviour

Students should appreciate that to fabricate falsify ormisrepresent data or to commit plagiarism constitutesunethical scientific behaviourey should be objec-tive unbiased and truthful in all aspects of their workand recognise the limits of their knowledge

ReferencesBl56 B Bloom et al lsquoTaxonomy of Educational Objectivesrsquo

Vol 1 Longman London 1956

DS09 lsquoDiploma Supplementrsquo (DS) European CommisionBrussels 2009 httpeceuropaeueducationhigher-educationdoc938_enhtm

EC07 EC Funding lsquoThe implementationof theBolognaProcessreforms intoPhysics Studies in Europersquo by EPS ref ASSOC-EDUC-2007-12 European Commission Brussels 2007

EC09a lsquoThe Bologna Process - Towards the EuropeanHigherEducation Arearsquo European Commission Brussels 2009httpeceuropaeueducationhigher-educationdoc1290_enhtmwwwondvlaanderenbehogeronderwijsbologna

EC09b lsquoThe EuropeanQualifications Framework (EQF)rsquo Euro-pean Commission Brussels 2009 httpeceuropaeueducationlifelong-learning-policydoc44_enhtmwwwondvlaanderenbehogeronderwijsbolognaqfqfasp

EC09c lsquoEuropean Credit Transfer and Accumulation Systemrsquo(ECTS) European Commission Brussels 2009httpeceuropaeueducationlifelong-learning-policydoc48_enhtm

Eu09a Eurydice Tools EuropeanGlossary on EducationEurydice Brussels 2009 httpeaceaeceuropaeueduca-tioneurydicetools_enphp

Eu09b lsquoHigher Education in Europe 2009 Developments in theBologna Processrsquo EAC EA P9 Eurydice Brussels 2009wwwondvlaanderenbehogeronderwijsbolognaconferencedocuments2009_Eurydice_reportpdf

Fe05 lsquoInquiries into EuropeanHigher Education in PhysicsrsquoVol 1 to 7 ed H Ferdinande et al EUPEN Gent 19972005wwweupenugentbe

IM07 L-30 lsquoClasse delle lauree in Scienze e Tecnologie fisichersquoItalian Ministry Decree Roma 2007httpbetafisicaunibaitLinkClickaspxfileticket=aCFiQgVLOPs3Damptabid=75ampmid=408amplanguage=it-IT

IU08 lsquoResolution on the Importance of Active Learning andHands-on Physics Educationrsquo IUPAP 26th General AssemblyTsukuba (JP) 2008 wwwiupaporggaga26handonrptpdf

JQ04 lsquoShared lsquoDublinrsquo descriptors for Short Cycle First CycleSecond Cycle and Third Cycle Awardsrsquo Joint Quality InitiativeDublin 2004 wwwjointqualitynlcontentdescriptorsCompletesetDublinDescriptorsdoc

LM07 lsquoRegulations for Study Programmes in Physicsrsquo Ministryof Higher Education Vilnius 2007

Ke09 Barbara M Kehm amp Achim Eckhardt lsquoThe implementa-tion of the Bologna Process into Physics Studies in Europe -The Bachelor Levelrsquo Project Report INCHER Kassel 2009

KF05 lsquoEmpfehlungen der Konferenz der Fachbereiche Physik(KFP) zu Bachelor- undMaster-Studiengaumlngen in PhysikrsquoKonferenz der Fachbereiche Physik Bad Honnef 2005wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

MS04 lsquoLa Physique en Licencersquo Rapport de perspectiveMission Scientifique Technique et PeacutedagogiqueMinistegravere Eacuteducation Nationale EnseignementSupeacuterieur Recherche Paris 2004www2enseignementsup-recherche gouvfrmstpphysique_licence_sfp_mstppdf

Ph09 lsquoPhysikmit integriertemDoktorandenkollegrsquo Friedrich-Alexander Universitaumlt Erlangen-Nuumlrnberg UniversitaumltRegensburg Max-Planck-Forschungsgruppe fuumlr OptikInformation und Photonik Erlangen-Nuumlrnberg-Regens-burg 2009 wwwenbphysikuni-erlangende

QA08 lsquoPhysics astronomy and astrophysicsrsquo Quality AssuranceAgency for Higher Education Gloucester 2008wwwqaaacukacademicinfrastructurebenchmarkstatementsPhysics08pdf

TU09a lsquoTuning Educational Structures in Europersquo Deusto ampGroningen 2009httptuningunideustoorgtuningeu

TU09b lsquoTuning Educational Structures in Europersquo Subject AreaPhysics Deusto amp Groningen 2009httptuningunideustoorgtuningeuindexphpoption=contentamptask=viewampid=31ampItemid=54

UN06 lsquoISCED 1997 International Standard Classificationof Educationrsquo Re-edition UNESCO-UIS Paris 2006wwwuisunescoorg

Vl07 L Vlsceanu L Gruumlnberg amp D Pacircrlea lsquoQuality Assuranceand Accreditation A Glossary of Basic Terms andDefinitionsrsquoUNESCO-CEPES Bucureti 2007wwwcepesropublicationspdfGlossary_2ndpdf

We09 UlrichWelbers lsquoModularisation and the development ofstudy programmes a German approachrsquo in lsquoEUA BolognaHandbook ndashldquoMaking BolognaWorkrsquo eds E Froment et alRaabe Stuttgart Berlin et al 2009wwwraabedegoaction=ProdDetailsampproduct_uuid=BS4L1L941WNBZQG5RSVTMG89YF3VMI64

EPS PUBLICATIONS 2009 11

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 13: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

1 - Membership of the bachelorspecification group

HonAss ProfHendrik Ferdinande (secretary)Universiteit Gent (BE)EPS Executive Committee Member

Professor em Peter MainUniversity of Nottingham (UK)Director Education amp ScienceInstitute of Physics (IoP)

Professor Gerd Ulrich NienhausKarlsruhe Institute of Technology [KIT] (DE)SpokespersonKonferenz der Fachbereiche Physik (KFP)Executive Board MemberDeutsche Physikalische Gesellscha (DPG)

Professor emUrbaan TitulaerJohannes-Kepler-Universitaumlt Linz (AT)EPS Physics Education Division Board Member

Professor em FriedrichWagner (chair)Ernst-Moritz-Arndt-Universitaumlt Greifswald (DE)EPS Past ampVice-president

Acknowledgementse bachelor specification group is greatly indebt toGJones (ImperialUK)RHenriegel (IoPUK) and LBellingham (QAA UK) for providing useful gui-dance We also acknowledge the essential commentsand improvements of the text by EdeWolf (NIKHEFamp VUA NL)M Knoop (UProvence FR)C Rossel(IBM Zuumlrich CH) and P Sauer (LeibnizUDE)

2 - European Benchmark for PhysicsBachelor Degree

Summaryis is a proposal to produce a common EuropeanBenchmark framework for bachelor degrees in Phy-sicse purpose is to help implement the commonEuropeanHigher EducationArea (EHEA) and to faci-litate co-operation and student exchange betweenEuropean Universities It is aimed at the level of anindicative listingwhich broadly specifies the commonprogramme which can be found in most physicsdegrees across Europe It also aims to represent thelevel of physics knowledge and skills physics depart-ments across Europe generally consider su$cient toadmit graduates of other universities to their masterprogrammes without supplementary requirementsexcept possibly for minor adaptations that do notlead to a net increase in the workload It is not inten-ded to either provide a fixed and detailed physicssyllabus or to replace the national quality assurancesystems in force in various countries

1 - IntroductionMost European countries have introduced a bachelordegree in response to the Bologna agreement and haveintroduced or are in the process of introducing mas-ters programmes In parallel to this countries areeither introducing or strengthening national (in somecases cross-border or regional) quality assurancemechanisms which are external to the university

Major changes to the structure of Physics degrees areassociated with

bulle Bologna agreementbulle introduction of the bachelormaster systembull External quality assurancemechanisms on a nationalor regional levelbullNational degree benchmarks for subject areas

Quality agencies are mainly concerned with genericcompetences (eg teamwork communication skills)

12 EPS PUBLICATIONS 2009

ANNEXES

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 14: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

and the general organisation of university studieseyare not usually prescriptive at the level of detailed curri-cula Indeed most national frameworks for physicsdegrees only provide a very general idea of the contentand are not su$ciently detailed for our purposeExamples of this are the German [1] (English version)andUK [2] national frameworks for Physics degrees Inthemain document an EPS working group issued sucha framework intended to be valid Europe wide [3]

ere have been extensive studies of physics curriculaby the EUPEN [4] (EUropean Physics Eucation Net-work) and its continuation the STEPS (StakeholdersTune European Physics Studies) and STEPS TWO [5]projects In addition theTUNINGproject has looked indetail at physics degrees and produced Reference Pointsfor the Design and Delivery of Degree Programmes inPhysics [6] Similar publications have been producedby the German Conference of Physics Departments[7] (in German) and the IOP (Institute of Physics) inthe UK [8]While there are many similar documentstheGerman andUKdocuments span the full spectrumof approaches to physics from the more rigorouslymathematical ldquoContinental Europeanrdquo approach to theless theoretically intensiveldquoAnglo-Saxonrdquoone

is is an attempt to provide amore detailed commonphysics syllabus but without specifying the content intoomuch detail as many dierent approaches are pos-sible to teach the same content and skillse level ofdetail involved lies between the general learning out-comes for a degree course and those for particularmodulescourse units

2 - Rationalee rationale for this project is to provide a generalreference point for Physics degrees to aid the imple-mentation of the Bologna changes and facilitateco-operation and student exchange between physicsdepartments across Europee aims are as follows

e programmes concerned may have a dierent formal titleIn many countries programmes called ldquoTechnical Physicsrdquo orldquoPhysics andhelliprdquo (egldquoAstronomyrdquo) are oered that satisfy thesebenchmarks either in full or with only minor exceptions otherprogrammes with such titles may not do so however

bull Provide a Europe wide reference set of benchmarksbullNot to be overly prescriptive allowing for variationsin teaching approachesbullConcentrating on physics content not general com-petences which are well covered in other documentsbull Specify the physics knowledge required for amasterslevel course in physicsbull Provide a ldquoquality markrdquo for Physics degreesbullHelp mobility both within bachelor degrees(SocratesErasmus typemobility) and between bache-lor andmaster degrees (Bologna type mobility)bull Provide a useful reference point especially for smal-ler countries and less well known universities or forbachelor students planning to enrol in a master pro-gramme elsewhere

Clearly if this is going to be a useful document it needsto be su$ciently detailed to be useful without imposinga rigid curriculumAll the following detailed structureneeds to be approached from a flexible perspective andnot applied in an inflexible manner General compe-tences should also be addressed explicitly in theprogramme either as an integrated part of some of thecontent oriented courses or in separate courses

3 - Overall structureOn the basis of the EUPEN and TUNING studies sixbroad areas of study or themes have been identifiedFive of these are essential for a physics degree andclearly compulsory and the sixth is provided for optio-nal minor specialisationse sixth theme can be aminor subject (or subjects) either related to Physicsor totally unrelated Examples of this are foreign lan-guage skills Chemistry Electronics Medical PhysicsAstronomy amp Astrophysics and Geophysics it mayalso contain courses on general or teaching skillsAnother alternative is a placement period in an out-side organisationis stream may also be omittedand the credits reassigned to other streams

is structure is based on a 3 year bachelor degreebutit could equally cover the first 3 years of an integrateddegree or even a 4 year bachelor In the case of a 4year bachelor degree it is possible that the credit allo-cations would be larger in some streams Creditallocations are indicative not precise values Most

EPS PUBLICATIONS 2009 13

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 15: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

modulescourse units on a degree programme shouldbe allocated to one area based on their content evenif they also cover part of another stream Howeveroccasionally they may need to be split between areas

e streams are indicated in the following table Ove-rall at least 140 of the normally 180 ECTS creditswould have to be in physics and maths that is in thefirst 5 streams Notional credit values for each streamare in the range 20-40with the exception of the optio-nal stream which is 0-40e tables are not intendedto specify a temporal order of the subjects or a grou-ping in modules or other units

Physics Bachelor degreeAt least 140 out of 180 ECTS credits

in physics ampmaths

Mechanics ampermodynamics (20-40 credits)Classical mechanicsermodynamics and kinetictheory Special relativity Advanced classical mecha-nics Background to quantummechanics

Optics amp Electromagnetism (20-40 credits)Oscillations amp waves Basic optics ElectromagnetismAdvanced Electrodynamics and Optics

Quantum Physics (20-40 credits)Quantummechanics Statistical mechanics Solid statephysicsAtomic nuclear and particle physics

Experimentallaboratory (20-40 credits)Laboratory work Project work

Mathematics amp computing (20-40 credits)Mathematics IT skills amp Modelling

Optional subjects (0-40 credits)Aminor subject (or subjects) either related to Physicsor totally unrelated

A more detailed structure for the benchmarks isgiven in the table on the following two pages Inorder to keep this table to a reasonable size thetopics have been given as headings which shouldbe understandable to physicists It has become usualto specify learning outcomes for particularmodules this is not done in this case to save spaceand avoid repetition Each of the items contained inthis listing will refer to several learning outcomesThe table should be considered as a core contentprogrammes will contain additional subjects ortreat some subjects in more depth than indicatedin the table So if a student changes university afterthe bachelor to pursue a master elsewhere he or shewill often have less knowledge and skills in somesubjects than students who completed their bache-lor at their new university but more in some othersubjects Such students may then be advised orsometimes even required to supplement their exis-ting knowledge in some subjects but this should bepossible by substitution for courses already coveredin his or her own bachelor programme or by res-tricting the choice of electives and not lead to a netincrease of the overall workload

In addition to general physics bachelor programmesdepartments may offer interdisciplinary or speciali-sed bachelor programmes (eg aimed at futureteachers of physics often combined with anothersubject or at other professional fields) Such pro-grammes are not primarily designed to prepare for ageneral physics master and may not contain all thesubjects listed in this document or treat them inthe breadth andor depth envisaged here In gene-ral there will be arrangements to grant graduates ofsuch programmes access to physics master pro-grammes as well such arrangements may involverestrictions on the electives chosen but sometimesalso ldquobridging coursesrdquo to be covered before orduring the master programme that amount to addi-tional credit requirements

4 - Detailed structuree following table relies heavily on the IOP docu-ment [8] from which most subject descriptions havebeen adopted

14 EPS PUBLICATIONS 2009

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 16: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

EPS PUBLICATIONS 2009 15

Mechanics andThermodynamics Optics amp Electromagnetism QuantumPhysics

20-40 ECTS credits 20-40 ECTS credits 20-40 ECTS credits

Classical mechanicsbull Newtonrsquos laws and conservation lawsincluding rotationbull Newtonian gravitation to the level ofKeplerrsquos laws

Thermodynamics and kinetic theory of gasesZeroth first and second laws of thermody-namics to includebull Temperature scales work internal energyand heat capacitybull Entropy free energies and the Carnot cyclebull Kinetic theory of gases andthe gas laws to the level of the van derWaalsequationbull The Maxwell-Boltzmann distributionbull Statistical basis of entropybull Changes of state

Special relativitybull to the level of Lorentz transformations andthe energy-momentum relationship

Advanced classical mechanics BasicLagrangian and Hamiltonianmechanics

Background to quantummechanicsbull Black body radiationbull Photoelectric effectbull Wave-particle dualitybull Heisenbergrsquos Uncertainty Principle

Oscillations ampwavesbull Free damped forcedandcoupledoscillationsto include resonanceandnormalmodesbull Waves in linear media to the level of groupvelocitybull Waves on strings sound waves and electro-magnetic wavesbull Doppler effect

Basic opticsbull Geometrical optics to the level of simpleoptical systemsbull The electromagnetic spectrumbull Interference and diffraction at single andmultiple aperturesbull Dispersionbyprismsanddiffractiongratingsbull Optical cavities and laser action

Electromagnetismbull Electrostatics andmagnetostaticsbull DC and AC circuit analysis to the level ofcomplex impedance transients and reso-nancebull Gauss Faraday Ampegravere Lenz and Lorentzlaws to the level of their vector expression

Advanced Electrodynamics and Opticsbull Maxwellrsquos equations and plane electromag-netic wave solution Poynting vectorbull Polarisation of waves andbehaviour at plane interfaces

QuantummechanicsSchroumldinger wave equation to includebull Wave function and its interpretationbull Standard solutions and quantum numbers tothe level of the hydrogen atombull Tunnellingbull Firstorder timeindependentperturbationtheory

Statistical mechanicsbull Bose-Einstein and Fermi-Dirac distributionsbull Density of states and partition function

Atomic nuclear and particle physicsbull Quantum structure and spectra of simpleatomsbull Nuclear masses and binding energiesbull Radioactive decay fission and fusionbull Pauli exclusion principle fermions andbosons and elementary particlesbull Fundamental forces and the StandardModel

Solid state physicsbull Mechanical properties of matter to includeelasticity and thermal expansionbull Inter-atomic forces and bondingbull Phonons and heat capacitybull Crystal structure and Bragg scatteringbull Electron theory of solids to the level of simpleband structurebull Semiconductors and dopingMagnetic properties of matter

Experimental amp laboratory work Mathematics amp computing Optional subjects

20-40 ECTS credits 20-40 ECTS credits 0-40 ECTS credits

Laboratory workbull plan an experimental investigationbull use apparatus to acquire experimental databull analyse data using appropriate techniquesbull determine and interpret themeasurementuncertainties (both systematic and random)in a measurement or observationbull report the results of an investigation andbull Understand how regulatory issues such ashealth and safety influence scientific experi-mentation and observation

Project workThe objectives of such project work willincludemost of the followingbull investigation of a physics-based or physics-related problembull planning management and operation ofan investigation to test a hypothesisbull development of information retrieval skillsbull carrying out a health and safety assessmentbull establishment of co-operative working prac-tices with colleaguesbull design assembly and testing of equipmentor softwaregeneration and informed analysis of dataand a critical assessment of experimental(or other) uncertainties

Mathematicsbull Trigonometric and hyperbolic functionscomplex numbersbull Series expansions limits and convergencebull Calculus to the level of multiple integralssolution of linear ordinary and partial differ-ential equationsbull Three-dimensional trigonometrybull Vectors to the level of div grad and curlrotdivergence theorem and Stokesrsquo theorembullMatrices to the level of eigenvalues andeigenvectorsbull Fourier series and transforms including theconvolution theorembull Probability distributions

IT skills ampModellingbull Word processing packagesbull Data analysis andmanipulation packagesbull Data calculation amp presentationbull Information searchingbull (A) Programming language(s)bull Modelling of physical systems

Aminor subject (or subjects) either related toPhysics or totally unrelated This streammayalso be omitted and the credits reassigned toother streams

Examples includebull Chemistrybull Electronicsbull Astronomy amp Astrophysicsbull Medical Physicsbull Geophysicsbull Biophysicsbull Meteorologybull Foreign language skills

This thememay also include courses on gener-ic and or teaching skills

Industrial PlacementSome degree programmesmay include aplacement in industry or other external organ-isation for up to one semester

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 17: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

PHYSICS BACHELOR STUDIES

5 - Implementatione present scheme has some analogies with the Euro-bachelorreg [9] model of the European Association ofChemical and Molecular Sciences However we do notpropose to follow their procedure in all particularsWesuggest physics departments self-certify their pro-grammes as being consistent with these benchmarksor not and if not give their reasonsWhen some sub-jects cannot be accommodated within the obligatorycourses theymight be oered as electivesWhen a stu-dent satisfies the benchmarks by choosing suchelectives or by taking voluntary courses the fulfilmentof the benchmarks may be certified individually egin the diploma supplementese statements could bemonitored in the course of existing quality assuranceprocedures Similarly we suggest departments usethese benchmarks to specify the knowledge and skillsthey require for admission to their masters pro-grammes they may deviate from them but shouldthen point out explicitly where their requirements forsome or all of their master programmes dier fromthose specified above

References[1] wwwasiindeenglishdownloadcrit_tc13pdf

[2] wwwqaaacukacademicinfrastructurebenchmark state-mentsPhysics08pdf

[3] ldquoA European Specification for Physics Bachelor Studiesrdquo EPSPublications 2009

[4] wwweupenugentbe

[5] wwwstepstwoeu

[6] wwwtuningunideustoorgtuningeuindexphpoption=com_docmanampItemid=59amptask=view_categoryampcatid=19amporder=dmdate_publishedampascdesc=DESC

[7] wwwkfp-physikdedokumentEmpfehlungen_Ba_Ma_Studiumpdf

[8] wwwioporgactivitypolicyDegree_Accreditationfile_26578pdf

[9] httpectn-assoccpefreurobachelor

is Annex 2 was draed by a task force ofWorkingGroup 1 of the STEPS TWO networke task force members werebull Eamonn Cunningham Dublin City University IE(Chair of Task Force)bull Ian Bearden Koslashbenhavns Universitet DKbull Radu Chisleag Universitatea POLITEHNICA dinBucureti RObullMaria Isabel Lopes Universidade de Coimbra PTbull Ryszard Naskrcki Uniwersytet imAdama Mickie-wicza Poznan PLbullUrbaan M Titulaer Johannes Kepler UniversitaumltLinzAT (Chair ofWorking Group 1)

e European Physical Society (EPS) is a not-for-profit representative organization whose purpose is topromote physics and physicists in Europe Created in1968theEPSprovides an international forum todiscussscience and policy issues of interest to its members

16 EPS PUBLICATIONS 2009

NOTES

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg

Page 18: AEUROPEAN SPECIFICATIONFOR ......PHYSICSBACHELORSTUDIES •have demonstrated knowledge and understan-ding in a field of study that builds upon their general secondary education,and

European Physical Society

6 rue des Fregraveres Lumiegravere bull 68200 Mulhouse bull Francetel +33 389 32 94 42 bull fax +33 389 32 94 49websitewwwepsorg