Lecture Mod Phys Fall 2014 NPG 3 Introduction Quantum Mechanics
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Transcript of Lecture Mod Phys Fall 2014 NPG 3 Introduction Quantum Mechanics
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8/12/2019 Lecture Mod Phys Fall 2014 NPG 3 Introduction Quantum Mechanics
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WELCOMEThe strange ( and beautiful ) world of
Quantum MechanicsVery
frightening
Justbeautiful!
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Newton thou ht that li ht was made u of
particles, but then it was discovered that itbehaves like a wave. Later, how ever (inthe beginning of twentieth century), it was
found, for example, behave like particle,respects it behave like a wave. So, it
..
The Feynman Lectures on Physics, Vol III
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Refraction of a corpuscle at a plane surface
o, o 0
X
P 1,E1 1
Conservation of momentumin x-component and energy
=
P 0 Sin 0 = P 1Sin 1Snells Law Sin 0 / Sin 1 = P 1/P 0 = mv1 / mv0 where m = mass
Sin 0 / Sin 1 = v1 / v0
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Two Slit experiments
With particles (bullets)
is easy to understand
- LUMPINESS!
1 I 12
I 2
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With waves water waves
1 I 12
2
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Waves interfere!NO LUMPINESS!
1 + 2 12
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With electrons
bullets - lumps1 12 I 12
I 2
INTERFERENCE!
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God doesno p ay
dice!
This type of behaviorwas observed first in
the case of light !
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History
Light is a beamof particles
Exhibitsinterference,
Newton Huygens
,hence waves
EinsteinIn photoelectric effect,
light behaves like particlesMaxwell
In my scattering expts,
Compton
g - eam o par c es
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D li
A oun irl?Whom do you see
in this picture?
Old woman?
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WAVE-PARTICLE DUALITY OF LIGHTIn 1924 Einstein wrote:- There are therefore now twotheories of light, both indispensable, and without anylo ical connection.
Evidence for wave-nature of light
Evidence for particle-nature of light Photoelectric effect Compton effect
are only explicable in terms of wave properties
Light is always detected as packets (photons); if we look,we never observe half a hoton
Number of photons proportional to energy density (i.e. tosquare of electromagnetic field strength)
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MATTER WAVES
De Broglie
We have seen that light comes in discrete units (photons) witharticle ro erties ener and momentum that are related to the
wave-like properties of frequency and wavelength.
n r nce ou s e rog e pos u a e a or nary ma er can avewave-like properties, with the wavelength related to momentum
p in the same way as for light
h =de Broglie relation
34
Plancks constant
pde Broglie wavelength .=
Prediction: We should see diffraction and interference of matter waves
,
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p = mv, m = mass, v = velocity
= 1/2 = , p = (2mqV) 1/2 , V= potential difference, q = charge
Only moving particles exhibit matter wavesarac er s cs Lighter particle-Longer wave length
Smaller speed-longer wave length Matter waves travels faster than speed of light in vacuum
hase velocit v > c
Matter waves are not real waves and there fore can not berepresented by wave displacement
The quantity whose variations make up matter waves iscalled the wave function where | |2 is the probability
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Estimate some de Broglie wavelengths
Wavelength of electron with 50eV kinetic energy2 2
10 p h h 2 .
2 2 2e e em m m K
= = = =
u3 , Mass 28mkT K = =
112.8 10 m3
h
MkT = =
Wavelength of Rubidium(87) atom at 50mK
61.2 10 m3
h
MkT = =
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COMPTON SCATTERING-
Compton
solid target, as function of wavelength for different angles.He won the 1927 Nobel prize.
X-ray source Crystal(selects
Collimator(selects angle)
wavelength)
Target
Result: peak in scattered radiationDetector
s ts to onger wave engt t an source.Amount depends on (but not on thetarget material). A.H. Compton, Phys. Rev. 22 409 (1923)