PHY520 Introduction to Quantum Mechanics

About myself:Kwok-Wai NgOffice: CP 385Telephone: 7-1782E-mail: kwng@uky.edu

Office hour: Mon 10:00-11:00

About this course

Time: Monday, Wednesday, and Friday 12:00-12:50 p.m.

Place: CP 183

Text book: Quantum Mechanics –Concepts and Applications, by NouredineZettili. (Publisher: John Wiley)

Grading policy

Homework 40%Test 1 15%Test 2 15%Final Examination 30%Total 100%

Syllabus

• Read syllabus carefully at home. Ask if you have any question.

• Please sign the class roll when it is passed to you.

• Evaluation window for this semester:13 April 2009 (Monday) to 29 April 2009 (Wednesday)

Some important plane wave parameters

v

λ t)-rki(

t)-i(kx

eA t),r(

:D-3eA t)(x,

:D-1

ω⋅

ω

=ψ

=ψ

vvv

Wave length λ:

λπ

=2 k

Frequency ν:

T1 and 2 =νπν=ω

vk or v =ωνλ=

Relationship between λ and ν:

Experiments showing particle property of electromagnetic waves

1. Black body radiation

2. Photoelectric effect

3. Compton effect

4. Pair production

Wave parameters:

Blackbody radiationA blackbody absorbs all radiation incident upon it. In reverse, it radiates electromagnetic wave when it is heated. The radiation spectrum depends on the temperature of the blackbody.

A model blackbody

Some classical properties of blackbody radiation

1. Wien’s Displacement Law gives the peak position:

T or K m 10 7685(51) 2.897 T

max

–3max

∝⋅×=

νλ

2. Stefan’s Law gives the area under curve:

black sonot for 1 blackperfect for 1 emissivity

KmJs105.670400 T

apower /Areradiation Total

4-2-1-8-

4

<==×=

=

εσ

σε

Attempt to get the exact equation of the spectral distribution ⇒ Rayleigh-Jeans Theory

3. Exact form? Wien’s Law (thermodynamicalderivation):

5

)()(uλλλ Tf

=

(infinite possible equations can satisfy this requirement!)

Energy in a BlackbodyIntroduce “density of states” N(ν) defined as the number of modes per unit frequency per volume. For electromagnetic plane waves, c=λν and N(ν)= 8πν2/c3.

The spectral density u(λ) is the total energy radiated per unit wavelength.

dd)V)E(N( )u( )V)E(N( )u(

d)(ud)u( : to from varibaleof Change λν

λλ=λ⇒νν=ν∴νν=λλλν

Choice of E(ν) matters! Rayleigh-Jeans classical approach:

Trouble!

5B

BTk 8 )u( Tk E )E(

λλπ

=λ⇒=><=ν

Planck’s quantum mechanical approach:

1e

c

h 8)u( 1e

h)E( Tk

h

3

3Tk

h

BB −

νπ=ν⇒

−

ν=ν νν

Perfect fit ⇒electromagnetic radiation is composed of small energy packets (quanta), each quanta has energy hν.

Photoelectric effect

UV Light

e-

A

V

Electron slowing down by going from a high potential to a low potential

+ High potential

Retarding voltage: As we crank up the retarding voltage, A will decrease. Eventually A will become 0 when V reaches the stopping voltage V0. From V0 we can calculate the kinetic energy K of the electrons.

e-e-

- Low potential

Experimental arrangement:

K=eV0

νW

Slop

e = h

K= hν - W

Findings:

The stopping voltage V0 (i.e. K) is independent of the intensity, but depends on the frequency of the incident wave.

Implication:

Light is composed of small energy packets (quanta), each quanta has energy hν.

Compton effectCompton effect describes the collision between an electron and a photon (X-ray).

φθν

ν’

Longer wavelength

Experimental results follow conservation of energy and momentum by assuming electromagnetic radiation as particles of E=hν and p=h/λ.

) cos-(1 mch '- φ=λλ=λ∆

In conclusion

In some experiments, a plane wave of frequency ν and wavelength λ behaves like a particle of energy E and momentum p, with

λ=ν=

h p and h E

Notes:1. ν and λ are wave parameters and E and p are particle parameters.

2. if [E] is the unit of energy and [p] is the unit of momentum, then the unit of h is [E]-s or [p]-m.