Post on 09-Aug-2020
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.