Density of modes:
N ( ) =
(, T ) =
c exp ( khT ) 1
Energy quantized in units of h where h = 6.626 1034 J s
Electrons and photons
Kmax = eV0 = h w
= c (1 cos
I. Blackbody radiation (1/2 week) Section 1.1
1. Cavity modes
2. Rayleigh-Jeans theory
3. Planck theory
II. Electrons and Photons (1/2 week)
1. Photoelectric effect Section 1.2
2. Compton effect Section 1.3
III. The Atomic Nucleus (1 week) Not in
Physics 137A Midterm #1 h = 1.055 1034 Js 0 = 8.85 1012 C2 /Jm c = 2.998 108 m/s me = 9.11 1031 Kg
Fall 2009 Wed. Oct. 7th e = 1.602 1019 C mp = 1.67 1027 Kg mn
1. (25 points) Answer the following questions succintly: (a) Describe Stefans law and Wiens di
Due: Friday, Nov. 6th
Problem Set # 9:
1. Use the result
2 n n!
exp(q 2 /2)
derived in class for the simple harmonic oscillator to generate 1 , 2 , 3 , and 4 .
2. Consider a simple harmonic oscillator in t
Due: Friday, Oct. 30th
Problem Set # 8:
1. A particle of mass m and energy E > 0 is incident on a 1-D square well potential V (x) = V0 (|x| < a),
V (x) = 0 (|x| > a).
(a) Show that the transmission coecient for the particl
Due: Friday, Oct. 23rd
Problem Set # 7:
1. For the potential step of height V0 at x = 0, show that, for energy eigenvalue E < V0 , the eigenfunction
can be written as
C cos k1 x C k2 sin k1 x x 0
Due: Friday, Oct. 16th
Problem Set # 6:
1. Prove the following operator identity involving commutator brackets:
[AB, C ] = A[B, C ] + [A, C ]B
Calculate the values of the following commutator brackets by allowing them to a
Due: Friday, Oct. 2nd
Problem Set # 5:
1. Problem 2.6 of Bransden and Joachain.
2. (The algebra in this problem is a bit tedious, but the end result is worth it!)
Consider the following wavefunction in 1D
(x, t) =
Due: Friday, Sept. 25th
Problem Set # 4:
1. Calculate the de Broglie wavelength of
(a) a mass of 1 g moving at the velocity of 1 m/s.
(b) a free electron having a kinetic energy of 200 eV.
(c) a free electron having a kine
Due: Monday, Sept. 21st
Problem Set # 3:
1. Calculate the magnetic moment (in mks units) generated by an electron in a circular Bohr orbit of
quantum number n in terms of n and appropriate fundamental constants.
Due: Monday, Sept. 14th
Reading: Sections 1.21.4 of Bransden & Joachain.
Problem Set # 2:
1. A photon of energy E undergoes Compton scattering with a free electron (rest mass m0 ) initially at rest.
(a) Find an expression
Due: Friday, Sept. 4th
Section 1.1 of Bransden & Joachain.
Wikipedia article on blackbody radiation.
Review spherical polar coordinates and the concept of solid angle.
Problem Set # 1:
1. Consider radiation in