PHYS 234: Quantum Physics 1 (Fall 2009)
Assignment 2
Issued: September 23, 2009
Due: 12.00pm, September 30, 2009
Drop-Box Physics Department, opposite to PHY 211A
1. Davisson and Germer Experiment
In the experiment of Davisson and Germer, (a) find the ang
PHYS 234: Quantum Physics 1 (Fall 2009)
Assignment 1 Solutions
Issued: September 16, 2009
Due: 12.00pm, September 23, 2009
1.) Photons [10 points]
An ultraviolet lightbulb emitting at 400 nm , and an infrared lightbulb emitting at 700 nm, each are
rated a
PHYS 234: Quantum Physics 1 (Fall 2009)
Assignment 3
Issued: September 30, 2009
Due: 12:00 noon, October 7, 2009
Drop-Box Physics Department, opposite to PHY 211A
Pauli Matrices (See sections 2.9-2.10 (Englert) of Section
2 of the UW-Courseware)
Pauli ope
PHYS 234: Quantum Physics 1 (Fall 2009)
Assignment 10
Issued: Nov 28, 2009
Due: 12:00 noon, Dec 4, 2009
Drop-Box Physics Department, opposite to PHY 211A
*The solutions to questions I and V have been updated.*
Grading Total number of points
Question 1: 20
HW #6 (221A), due Oct 6, 4pm
1. Apply the WKB method to the harmonic oscillator.
(a) Show that the energy levels comes out exactly.
(b) Work out the wave functions for n = 1, n = 10, and n = 20, and
compare to the exact results. (Hint: Mathematica knows H
HW #9 (221A), due Nov 10, 4pm
1. Consider a three-dimensional isotropic harmonic oscillator with Hamiltonian
1
3
p~2
2 2
+ m ~x = ~ ~a ~a +
.
H=
2m 2
2
(This is the starting point of the shell model of nuclei.) Answer the
following questions.
(a) Clearly,
HW #8 (221A), due Nov 3, 4pm
1. Consider the SternGerlach experiment for spin 1. When the atom
enters with Jz = +~ in the magnetic field along the x axis, determine
the relative strengths of three lines that correspond to Jx = +~, 0, ~.
2. The quadrupole
HW #7 (221A), due Oct 13, 4pm
1. Consider a free particle with Hamiltonian H = p~2 /2m.
(a) Derive the propagator (Sakurais Eq. (2.5.16)
3/2
m
im(~x00 ~x0 )2
00 00 0 0
exp
.
h~x , t |~x t i =
2i~(t00 t0 )
2~(t00 t0 )
(1)
(b) Show that the exponent is noth
HW #11 (221A), due Dec 1, 4pm
1. We would like to find the ground-state wave function of a particle in
the potential V = 50(ex 1)2 with m = 1, ~ = 1. In this case, The
true ground-state energy is known to be E0 = 39/8. Plot the form
of the potential. Note
HW #5 (221A), due Sep 29, 4pm
1. Answer the following questions on the harmonic oscillator H =
1
m 2 X 2 .
2
P2
2m
+
(a) Verify that the Hamiltonian can
be recast to the form H = ~(N +
p m
P
1
X + i m
.
), where N = a a and a =
2
2~
(b) Write down the con
HW #3 (221A), due Sep 15, 4pm
1. Answer the following questions about the spin operators using their
matrix representation,
h
Sx =
2
0 1
1 0
!
,
h
Sy =
2
0 i
i 0
!
,
h
Sz =
2
1 0
0 1
!
.
(1)
(a) Show the commutation relations [Si , Sj ] = i
hijk Sk .
~ al
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