lecture mod phys fall 2014 npg 3 introduction quantum mechanics

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)

lecture mod phys fall 2014 npg 3 introduction quantum mechanics

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