ADVANCED MULTIPLE CHOICE QUESTIONS IN QUANTUM PPHYSICS College of Science/ Department of Physics

P- FACTS 2015

Third Year

PHY 351 QUANTUM MECHANICS ISECTION A

1. What is the name of the relationship between the peak wavelength for a black body radiation and

its temperature; what sort of wavelength is it?

A. Planck’s law, luminosity = fourth power of the temperature

B. Bohr’s law, atoms will have quantized electrons states proportional to their temperature

C.Wein’s law, that the peak wavelength is inversely proportional to the body’s temperature

D. Helmholtz Principle; as a body grows smaller, it must heat up

2. If the surface of Venus is, on average, about three times hotter than the surface of Mars, how does

the infrared output of the two planets occur?

A. Venus gives off three times as much energy, but at about the same wavelength

B. Mass gives off three times less energy, but at three times shorter wavelength

C. Venus gives off about the same total amount of energy, but at three times longer wavelength

D. Venus infrared radiation peaks at 1/3 that of Mars in wavelength, and far exceeds that of Mars in

intensity.

3. What wavelength range does the 5,800 K temperature of the Sun’s photosphere cause most solar

radiation to fall?

A. Ultraviolet

B. Visible

C. Infrared

D. Radio

4. Use Wien’s Law to find the peak radiation for a star whose surface temperature is 2,900K.

In what form of energy would this peak fall?

A. 100,000nm in the microwaves

B. 1000nm in the near infrared

C. 100nm in the ultraviolet

D. 100nm in the X-rays

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5. A newly formed white dwarf has a peak in its spectrum at 145nm, in the ultraviolet. Find it

surface temperature.

A. 200K

B. 2,000K

C. 20,000K

D. 200,000K

6. An object has a temperature of 1200K. Find the wavelength (nm) at which the maximum

radiation intensity will be emitted.

A. 2420nm

B. 2000um

C. 3660nm

D. 4200um

7. The momentum of a photon of frequency 109cycles is

A. 2.2× 1033 kg .m/ s

B. 6.6×10−26 kg .m /s

C. 1.5×107 kg .m /s

D. 7.3×1029 kg . m /s

8. The units of the Planck constant h are those of:

A. energy

B. power

C. momentum

D. angular momentum

E. frequency

9. Which of the following electromagnetic radiations has photons with the greatest energy?

A. blue light

B. yellow light

C. x rays

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D. radio waves

E. microwaves

10. Which of the following electromagnetic radiations has photons with the greatest momentum?

A. blue light

B. yellow light

C. x rays

D. radio waves

E. microwaves

11. Radio waves of wavelength 300m have a frequency of:

A. 10−3 kHz

B. 500 kHz

C. 1MHz

D. 9MHz

E. 108 kHz

12. Visible light has a frequency of about:

A. 5 × 1018 Hz

B. 5 × 1016 Hz

C. 5 × 1014 Hz

D. 5 × 1012 Hz

E. 5 × 1010 Hz

13. The speed of light in vacuum is about:

A. 1100 ft/s

B. 93 × 106 m/s

C. 6 × 1023 m/s

D. 3 × 1010 cm/s

E. 186, 000 mph

14. Of the following human eyes are most sensitive to:

A. red light

B. violet light

C. blue light

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D. green light

E. none of these (they are equally sensitive to all colors)

15. Select the correct statement:

A. ultraviolet light has a longer wavelength than infrared

B. blue light has a higher frequency than x rays

C. radio waves have higher frequency than gamma rays

D. gamma rays have higher frequency than infrared waves

E. electrons are a type of electromagnetic wave

16. A point source emits electromagnetic energy at a rate of 100W. The intensity 10m from the

source is:

A. 10W/m2

B. 1.6W/m2

C. 1W/m2

D. 0.024W/m2

E. 0.080W/m2

17. The light intensity 10m from a point source is 1000W/m2. The intensity 100m from the same

source is:

A. 1000W/m2

B. 100W/m2

C. 10W/m2

D. 1W/m2

18. A photon in light beam A has twice the energy of a photon in light beam B. The ratio pA/pB

of their momenta is:

A. 1/2

B. 1/4

C. 1

D. 2

E. 4

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19. In a photoelectric effect experiment the stopping potential is:

A. the energy required to remove an electron from the sample

B. the kinetic energy of the most energetic electron ejected

C. the potential energy of the most energetic electron ejected

D. the photon energy

E. the electric potential that causes the electron current to vanish

20. In a photoelectric effect experiment at a frequency above cut off, the stopping potential is

proportional to:

A. the energy of the least energetic electron before it is ejected

B. the energy of the least energetic electron after it is ejected

C. the energy of the most energetic electron before it is ejected

D. the energy of the most energetic electron after it is ejected

E. the electron potential energy at the surface of the sample

21. In a photoelectric effect experiment at a frequency above cut off, the number of electrons

ejected is proportional to:

A. their kinetic energy

B. their potential energy

C. the work function

D. the frequency of the incident light

E. the number of photons that hit the sample

22. In a photoelectric effect experiment no electrons are ejected if the frequency of the incident

light is less than A/h, where h is the Planck constant and A is:

A. the maximum energy needed to eject the least energetic electron

B. the minimum energy needed to eject the least energetic electron

C. the maximum energy needed to eject the most energetic electron

D. the minimum energy needed to eject the most energetic electron

E. the intensity of the incident light

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23. The work function for a certain sample is 2.3 eV. The stopping potential for electrons ejected

from the sample by 7.0 × 1014-Hz electromagnetic radiation is:

A. 0

B. 0.60V

C. 2.3V

D. 2.9V

E. 5.2V

24. The stopping potential for electrons ejected by 6.8×1014-Hz electromagnetic radiation incident

on a certain sample is 1.8V. The kinetic energy of the most energetic electrons ejected and

the work function of the sample, respectively, are:

A. 1.8 eV, 2.8 eV

B. 1.8 eV, 1.0 eV

C. 1.8 eV, 4.6 eV

D. 2.8 eV, 1.0 eV

E. 1.0 eV, 4.6 eV

25. Separate Compton effect experiments are carried out using visible light and x rays. The

scattered radiation is observed at the same scattering angle. For these experiments:

A. the x rays have the greater shift in wavelength and the greater change in photon energy

B. the two radiations have the same shift in wavelength and the x rays have the greater change

in photon energy

C. the two radiations have the same shift in wavelength and the visible light has the greater

change in photon energy

D. the two radiations have the same shift in wavelength and the same change in photon energy

E. the visible light has the greater shift in wavelength and the greater shift in photon energy

26. In Compton scattering from stationary particles the maximum change in wavelength can be

made smaller by using:

A. higher frequency radiation

B. lower frequency radiation

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C. more massive particles

D. less massive particles

E. particles with greater charge

27.Of the following, Compton scattering from electrons is most easily observed for:

A. microwaves

B. infrared light

C. visible light

D. ultraviolet light

E. x rays

28. In Compton scattering from stationary electrons the largest change in wavelength occurs when

the photon is scattered through:

A. 0◦

B. 22.5◦

C. 45◦

D. 90◦

E. 180◦

29. In Compton scattering from stationary electrons the frequency of the emitted light is

independent

of:

A. the frequency of the incident light

B. the speed of the electron

C. the scattering angle

D. the electron recoil energy

E. none of the above

30. In Compton scattering from stationary electrons the largest change in wavelength that can

occur is:

A. 2.43 × 10−15 m

B. 2.43 × 10−12 m

C. 2.43 × 10−9 m

D. dependent on the frequency of the incident light

E. dependent on the work function

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31.Electromagnetic radiation with a wavelength of 5.7×10−12 m is incident on stationary electrons.

Radiation that has a wavelength of 6.57 × 10−12 m is detected at a scattering angle of:

A. 10◦

B. 121◦

C. 40◦

D. 50◦

E. 69◦

32. Consider the following:

1. a photoelectric process in which some emitted electrons have kinetic energy greater

than hf, where f is the frequency of the incident light.

2. a photoelectric process in which all emitted electrons have energy less than hf.

33. Compton scattering from stationary electrons for which the emitted light has a wavelength

that is greater than that of the incident light.

4. Compton scattering from stationary electrons for which the emitted light has a wavelength

that is less than that of the incident light.

The only possible processes are:

A. 1

B. 3

C. 1 and 3

D. 2 and 3

E. 2 and 4

33. J. J. Thompson's measurement of e/m for electrons provides evidence of the:

A. wave nature of matter

B. particle nature of matter

C. wave nature of radiation

D. particle nature of radiation

E. transverse wave nature of light

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34.Evidence for the wave nature of matter is:

A. electron diffraction experiments of Davisson and Germer

B. Thompson's measurement of e/m

C. Young's double slit experiment

D. the Compton effect

E. Lenz's law

35. Which of the following is NOT evidence for the wave nature of matter?

A. The photoelectric effect

B. The diffraction pattern obtained when electrons pass through a slit

C. Electron tunneling

D. The validity of the Heisenberg uncertainty principle

E. The interference pattern obtained when electrons pass through a two-slit system

36. Of the following which is the best evidence for the wave nature of matter?

A. The photoelectric effect

B. The Compton effect

C. The spectral radiancy of cavity radiation

D. The relationship between momentum and energy for an electron

E. The reflection of electrons by crystals

37. free electron and a free proton have the same kinetic energy. This means that, compared to

the matter wave associated with the proton, the matter wave associated with the electron has:

A. a shorter wavelength and a greater frequency

B. a longer wavelength and a greater frequency

C. a shorter wavelength and the same frequency

D. a longer wavelength and the same frequency

E. a shorter wavelength and a smaller frequency

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38. A free electron and a free proton have the same momentum. This means that, compared to

the matter wave associated with the proton, the matter wave associated with the electron:

A. has a shorter wavelength and a greater frequency

B. has a longer wavelength and a greater frequency

C. has the same wavelength and the same frequency

D. has the same wavelength and a greater frequency

E. has the same wavelength and a smaller frequency

39. A free electron and a free proton have the same speed. This means that, compared to the

matter wave associated with the proton, the matter wave associated with the electron:

A. has a shorter wavelength and a greater frequency

B. has a longer wavelength and a greater frequency

C. has the same wavelength and the same frequency

D. has the same wavelength and a greater frequency

E. has a longer wavelength and a smaller frequency

40. Consider the following three particles:

1. a free electron with speed v0

2. a free proton with speed v0

3. a free proton with speed 2v0

Rank them according to the wavelengths of their matter waves, least to greatest.

A. 1, 2, 3

B. 3, 2, 1

C. 2, 3, 1

D. 1, 3, 2

E. 1, then 2 and 3 tied

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41. Consider the following three particles:

1. a free electron with kinetic energy K0

2. a free proton with kinetic energy K0

3. a free proton with kinetic energy 2K0

Rank them according to the wavelengths of their matter waves, least to greatest.

A. 1, 2, 3

B. 3, 2, 1

C. 2, 3, 1

D. 1, 3, 2

E. 1, then 2 and 3 tied

42. A free electron has a momentum of 5.0 × 10−24 kg · m/s. The wavelength of its wave function

is:

A. 1.3 × 10−8 m

B. 1.3 × 10−10 m

C. 2.1 × 10−11 m

D. 2.1 × 10−13 m

E. none of these

43. The frequency and wavelength of the matter wave associated with a 10-eV free electron are:

A. 1.5 × 1034 Hz, 3.9 × 10−10 m

B. 1.5 × 1034 Hz, 1.3 × 10−34 m

C. 2.4 × 1015 Hz, 1.2 × 10−9 m

D. 2.4 × 1015 Hz, 3.9 × 10−10 m

E. 4.8 × 1015 Hz, 1.9 × 10−10 m

44. If the kinetic energy of a non-relativistic free electron doubles, the frequency of its wave

function changes by the factor:

A. 1/√2

B. 1/2

C. 1/4

D. √2

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E. 2

45. A non-relativistic free electron has kinetic energy K. If its wavelength doubles, its kinetic

energy is:

A. 4K

B. 2K

C. still K

D. K/2

E. K/4

46. The probability that a particle is in a given small region of space is proportional to:

A. its energy

B. its momentum

C. the frequency of its wave function

D. the wavelength of its wave function

E. the square of the magnitude of its wave function

47. ψ(x) is the wave function for a particle moving along the x axis. The probability that the

particle is in the interval from x = a to x = b is given by:

A. ψ(b) − ψ(a)

B. |ψ(b)|/|ψ(a)|

C. |ψ(b)|2/|ψ(a)|2

D. ∫ ψ(x) dx

E.∫ |ψ(x)|2 dx

48. The significance of |ψ|2 is:

A. probability

B. energy

C. probability density

D. energy density

E. wavelength

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49. Maxwell's equations are to electric and magnetic fields as equation is to the wave function

for a particle.

A. Einstein's

B. Fermi's

C. Newton's

D. Schrodinger's

E. Bohr's

50. free electron in motion along the x axis has a localized wave function. The uncertainty in

its momentum is decreased if:

A. the wave function is made more narrow

B. the wave function is made less narrow

C. the wave function remains the same but the energy of the electron is increased

D. the wave function remains the same but the energy of the electron is decreased

E. none of the above

51. The uncertainty in position of an electron in a certain state is 5×10−10 m. The uncertainty in

its momentum might be:

A. 5.0 × 10−24 kg · m/s

B. 4.0 × 10−24 kg · m/s

C. 3.0 × 10−24 kg · m/s

D. all of the above

E. none of the above

52. The unit of Bohr radius is

A. m

B. m-1

C. ms

D. Js

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53. If a wave function ψ for a particle moving along the x axis is normalized, then:

A. ∫|ψ|2 dt = 1

B.∫|ψ|2 dx = 1

C. ∂ψ/∂x = 1

D. ∂ψ/∂t = 1

E. |ψ|2 = 1

54. An electron in an atom initially has an energy 5.5 eV above the ground state energy. It drops

to a state with energy 3.2 eV above the ground state energy and emits a photon in the process.

The wave associated with the photon has a wavelength of:

A. 5.4 × 10−7 m

B. 3.0 × 10−7 m

C. 1.7 × 10−7 m

D. 1.15 × 10−7 m

E. 1.0 × 10−7 m

55. An electron in an atom drops from an energy level at −1.1 × 10−18 J to an energy level at

−2.4 × 10−18 J. The wave associated with the emitted photon has a frequency of:

A. 2.0 × 1017 Hz

B. 2.0 × 1015 Hz

C. 2.0 × 1013 Hz

D. 2.0 × 1011 Hz

E. 2.0 × 109 Hz

56. An electron in an atom initially has an energy 7.5 eV above the ground state energy. It drops

to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the

process. The momentum of the photon is:

A. 1.7 × 10−27 kg · m/s

B. 2.3 × 10−27 kg · m/s

C. 4.0 × 10−27 kg · m/s

D. 5.7 × 10−27 kg · m/s

E. 8.0 × 10−27 kg · m/s

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57. The binding energy of an electron in the ground state in a hydrogen atom is about:

A. 13.6 eV

B. 3.4 eV

C. 10.2 eV

D. 1.0 eV

E. 27.2 eV

58. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron

and proton. Then the ground state energy is −13.6 eV. The energy of the first excited state is:

A. 0

B. −3.4 eV

C. −6.8 eV

D. −9.6 eV

E. −27 eV

59. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron

and proton. Then the ground state energy is −13.6 eV. The negative sign indicates:

A. the kinetic energy is negative

B. the potential energy is positive

C. the electron might escape from the atom

D. the electron and proton are bound together

E. none of the above

60. When a hydrogen atom makes the transition from the second excited state to the ground state

(at −13.6 eV) the energy of the photon emitted is:

A. 0

B. 1.5 eV

C. 9.1 eV

D. 12.1 eV

E. 13.6 eV

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61. According to the de Broglie s hypothesis of matter waves, the concepts of energy, momentum ‟

and wavelength are applicable to

A. moving particles but not to radiation (photon).

B. moving particles as well as to radiation (photon).

C. radiation (photon) but not to moving particles

C. neither to moving particles nor to radiation (photon).

62. Probabilistic interpretation of matter waves (as in the double slit experiment) was given by

A de Broglie

Max Born

Albert Einstein

Richard Feynman

W. Heisenberg

63. Phase velocity Vp of a wave is expressed as

A Vp = ω / k where ω = Angular frequency, k = propagation constant of the wave

A. where λ = wavelength and T = period of the wave

B. Vp = E/p where E = Energy, p= Momentum of the particle

C. No relation between Phase velocity and Group velocity

64. A particle has position (x, y, z) and corresponding momenta (px, py, pz). According to

Heisenberg s Uncertainty principle, following observables cannot be measured simultaneously.‟

A. x and p x

B. x and p y

C. p y and p z

D. x and z

65. According to Heisenberg s Uncertainty principle, Indeterminism in the measurement of ‟

canonically conjugate variables is due to

A. imperfection in measuring instruments

B. imperfection in measurement method

C. the indeterminism inherent in the quantum world itself

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D. all reasons

66. Canonically conjugate variables are

Position q and corresponding momentum p (in terms of generalized co-ordinates)

Energy E and Time t

Angular Position θ and Angular momentum L

None of these

67. Wave function Ψ of a particle is

a real quantity

a complex quantity

an imaginary quantity

any one of these

68. Which of the following quantities are complex quantities?

A. Wave function Ψ of a particle

B. Probability of a particle having Wave function Ψ

C. Probability Density of a particle having Wave function Ψ

D. Probability Current of a particle having Wave function Ψ

69. The wave function Ψ of the particle is

A. a solution to the wave equation

B. not a mathematical function

C. not a variable quantity

D. goes through repeating, periodic maxima and minima or oscillations

70. The probability current of a particle is

dependent on time.

number of particles per unit volume per unit time.

not a real quantity

always positive

71. The time-independent Schrödinger equation

is a partial differential equation

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involves only one independent variable r

can be derived from time-dependent Schrödinger equation

has solutions which are the stationary states.

72. Operators in quantum physics

A are used to represent physical observables in classical physics

A. are used to translate equations in classical physics into equations of quantum physics c)

corresponding to canonically conjugate variables commute.

B. are nonlinear, hermitian corresponding to classical dynamical variables

73. The continuity equation in quantum physics implies

A the conservation of probability

A. equation of the continuous functions

B. the conservation of wavefunction

C. the conservation of momentum of the particle

74. The time evolution equation of the expectation values of position and momentum of a quantum

mechanical particle is given by

A Continuity Equation

A. Ehrenfest’s Theorem

B. Divergence theorem (Green’s Second Theorem),

C. Schrödinger equation

75. To be physically acceptable, a quantum-mechanical wave-function must be

A single-valued

B finite everywhere

C continuous

D any of A, B, C

E all of A, B, C.

76. Consider a quantum-mechanical eigenvalue equation

A ^à n = a n à n

The operator A^ must be

A the Hamiltonian

B the angular momentum

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C the linear momentum

D expressed in spherical polar coordinates

E. Hermitian.

77. The physical significance of the eigenvalue an is

A a possible result of measurement of the dynamical variable A^

B the uncertainty in the measurement of A^

C the statistical average of a large number of measurements of A^

D the square of the wavefunction Ãn

E the relative probability of the value an.

78. The work function of a metal may be defined as

A. the minimum frequency of the incident electromagnetic radiation required to cause

Photoelectric emission.

B. the minimum wavelength of the incident electromagnetic radiation required to cause

Photoelectric emission.

C. the minimum energy of photons incident on a surface required to cause photoelectric

Emission.

D. the minimum energy required to take an electron from the interior to the surface to cause

photoelectric emission

79. The de Broglie wavelength of a particle that has kinetic energy E k is λ. The wavelength λ is

Proportional to

A. E k.

B. 1Ek

C.1

√Ek

D. E k

80. The Bohr model of the hydrogen atom is able to

A. predict accurate values for some of the wavelengths in the spectrum of atomic hydrogen.

B. account for the detailed structure of the spectral lines in the spectrum of atomic hydrogen.

C. explain the relative intensity of the different spectral lines in the spectrum of atomic hydrogen.

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D. be extended to predict accurately, some of the wavelengths in the spectrum of oxygen

81. An electron of mass me and a proton of mass mp are moving with the same speed. The de

Broglie wavelengths associated with the electron and with the proton are λe and λp

prespectively. The ratio λp

λe is equal to

A. mp

me

B.me

mp

C. √m p

me

D. √ me

mp

82. What is the value of the commutator [ Lx Ly , Lz ] ?

A. iћ (Lx2−Ly

2)

B. (Lx2−Ly

2)

C. −(Lx2−L y

2)

D. iћ (Lx2−Ly

2)

83. Given that J 2=J x

2+J y

2+J z

2, What is the value of [J2 , J x ]

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A. iћ (Lx2−Ly

2)

B. (Lx2−Ly

2)

C. 0

D. iћ (Lx2−Ly

2)

84. An operator is a quantity that acts on a wave function and multiplies the wave function by

constant known as the Eigen value of the operator as shown

A ̃ψ=λψ

Given that A=[0 1 −11 1 0

−1 0 1 ] , find λ

A. λ = -1or 2

B. λ = 1or 2

C. λ = -1or- 2

D. λ = -1or -2

85. Find the determinant of the operator A=[0 1 −11 1 0

−1 0 1 ]A. -2

B. 2

C. 1

D. -1

POSSBLE ANSWERS

Please don’t chew the answers, rather understand the concepts and basic calculations

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1 C 21 E 41 B 61 B 81 B

2 D 22 D 42 B 62 A 82 A

3 B 23 B 43 D 63 A 83 C

4 B 24 B 44 E 64 C 84 A

5 C 25 B 45 E 65 C 85 A

6 A 26 C 46 E 66 A

7 A 27 E 47 E 67 B

8 D 28 E 48 C 68 C

9 C 29 E 49 D 69 A

10 C 30 B 50 B 70 C

11 C 31 D 51 D 71 C

12 C 32 D 52 A 72 A

13 D 33 B 53 B 73 D

14 D 34 A 54 A 74 B

15 D 35 A 55 B 75 E

16 E 36 E 56 B 76 E

17 C 37 D 57 A 77 A

18 D 38 D 58 B 78 C

19 E 39 E 59 D 79 C

20 D 40 B 60 D 80 A

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PREPARED BY:

PROFESSOR FUAKYE ERIC GYABENG

2015/2016 ACADEMIC YEAR: BSC. PHYSICS (KNUST)

For more info

Contact: 0501373999/ WhatsApp 0207746514

ALL THE BEST IN YOUR EXAMS

Caution: Don’t Rely On It. LEARN!!!!

Caution: Don’t Rely On It. LEARN!!!!

Caution: Don’t Rely On It. LEARN!!!!

Caution: Don’t Rely On It. LEARN!!!!

Caution: Don’t Rely On It. LEARN!!!!

Caution: Don’t Rely On It. LEARN!!!!

References or Further materials for reading

1. Introduction to Quantum mechanics I, Mr. Isaac Nkrumah, KNUST 2014

2. Multiple choice questions in quantum physics, Fuakye Eric, KNUST 2014

3. Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles. 2nd Edition, Robert

Eisberg and Robert Resnick, John Wiley and Sons, New York 1985.4. Introductory quantum mechanics. 9th Ed. Richard L. Liboff, Addison-Wesley Publishing

Company, Califonia, 1989.5. Quantum mechanics, 2nd Ed. Amit Goswani Wm C., Brown Publishers, London, 1997.6. Physics for scientist and Engineers with modern Physics. 4th Ed. Douglas C. Giancoli,

Pearson

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