Quantum Mechanics
Solution Set 10
Due: 12 November 2014
Reading: Shankar, Section 16.2 and Chapter 7. Lecture notes, Sections 6.4-6.5 and Chapter
7.
49. a)Apply the WKB method to estimate the bound state energies for a particle moving in
the following pot
Quantum Mechanics
Solution Set 11
Due: 19 November 2014
Reading: Shankar, Chapter 8 and Lecture Notes, Chapter 8.
54. a) S, Exercise 7.4.2; b) S, Exercise 7.4.3; c) S, Exercise 7.4.4.
Solution:
a) It is immediate that n|x|n = n|p|n = 0 because x, p are li
Quantum Mechanics
Problem Set 3
Due: 17 September 2014
Reading: Shankar Sections 1.8-1.9; Lecture notes, Sections 2.7-2.8. Try to do as many of the
exercises in the text as you can. However, turn in only the ones that I assign!
11. Suppose a linear operat
Quantum Mechanics
Problem Set 2
Due: 9 September 2015
Reading: Shankar Sections 1.5-1.8 and 4.2; Lecture notes, Sections 2.5-2.7. Try to do as
many of the exercises in the text as you can. However, turn in only the ones that I assign!
7. Show that both th
Quantum Mechanics
Problem Set 12
Due: 2 December 2015
Reading: Shankar, Chapter 7,10 and Lecture Notes, Chapter 7, 9.
61. Consider the motion of a particle of charge Q in a uniform magnetic eld B = B z .
a) Find a vector potential for B with Ax = Az = 0,
Quantum Mechanics
Problem Set 13
Due: 9 December 2015
Reading: Shankar, Chapter 11 and Lecture Notes, Chapters 8-10.
66. a) S, Exercise 10.3.2; b) S, Exercise 10.3.3; c) S, Exercise 10.3.6.
67. In this problem we explore the relation between momentum and
Quantum Mechanics
Problem Set 1
Due: 2 September 2015
This and all future homework will be posted on the course webpage:
http:/www.phys.u.edu/thorn/homepage/qminfo.html
In the homework assignments, I will refer to problems in Shankar by prexing the proble
Quantum Mechanics
Solution Set 10
Due: 13 November 2015 (Note that this is a Friday since Wednesday is Veterans day.)
Reading: Chapter 7. Lecture notes, Chapter 7.
53. a) S, Exercise 7.4.2; b) S, Exercise 7.4.3; c) S, Exercise 7.4.6.
a) It is immediate th
Quantum Mechanics
Problem Set 3
Due: 16 September 2015
Reading: Shankar Sections 1.8-1.9; Lecture notes, Sections 2.7-2.9. Try to do as many of the
exercises in the text as you can. However, turn in only the ones that I assign!
12. Suppose a linear operat
Quantum Mechanics
Problem Set 9
Due: 4 November 2015
Reading: Shankar, Continue Chapter 5, and section 16.2; Lecture notes, Sections 6.4-6.5 and
start Chapter 7.
47. An interesting limit of a square well or barrier potential can be described as a delta
fu
Quantum Mechanics
Problem Set 4
Due: 23 September 2015
Reading: Shankar Sections 1.8-1.10,9.1-9.3; Lecture notes, Sections 2.8-2.12.
18. Show that an n n matrix (a) is necessarily diagonal if it commutes with all diagonal
n n matrices and (b) is necessari
Quantum Mechanics
Problem Set 5
Due: 30 September 2015
Reading: Shankar, Chapter 4 and Sections 2.1-2.6; Lecture notes, Sections 3.1-3.6.
24. S, Exercise 4.2.1
25. a) S, Exercise 4.2.2; b) S, Exercise 4.2.3.
26. Consider a photon moving along the z axis,
Quantum Mechanics
Solution Set 9
Due: 4 November 2015
Reading: Shankar, Continue Chapter 5, and section 16.2; Lecture notes, Sections 6.4-6.5 and
start Chapter 7.
47. An interesting limit of a square well or barrier potential can be described as a delta
f
Quantum Mechanics
Problem Set 8
Due: 28 October 2015
Reading: Shankar, Chapter 5; Lecture notes, Chapter 5 and Sections 6.3-6.4.
41. (Spreading of a Wave Packet). Consider a particle in a state described by the initial
wave function
3/4
1
2
2
er /2x .
hr|
Quantum Mechanics
Solution Set 7
Due: 14 October 2015
Reading: Shankar, Chapters 2 and 6; Lecture notes, Chapters 3 and 4.
36. In class we defined canonical transformations q, p Q, P as those which leave the
Poisson Brackets invariant
cfw_f, gQ.P = cfw_f,
Quantum Mechanics
Solution Set 6
Due: 7 October 2015
Reading: Shankar, Finish Chapter 2; Lecture notes, Finish Chapter 3, Sections 4.1-4.4
29. Start with the Lagrangian for a relativistic particle moving in an electromagnetic field
B = A, E = A/c,
q
Q
2
(
Quantum Mechanics
Solution Set 5
Due: 30 September 2015
Reading: Shankar, Chapter 4 and Sections 2.1-2.6; Lecture notes, Sections 3.1-3.6.
24. S, Exercise 4.2.1
Solution:
(1) Since Lz is diagonal,its eigenvalues, which are the possible values a measuremen
Quantum Mechanics
Solution Set 4
Due: 23 September 2015
Reading: Shankar Sections 1.8-1.10,9.1-9.3; Lecture notes, Sections 2.8-2.12.
18. Show that an n n matrix (a) is necessarily diagonal if it commutes with all diagonal
n n matrices and (b) is necessar
Quantum Mechanics
Solution Set 3
Due: 16 September 2015
Reading: Shankar Sections 1.8-1.9; Lecture notes, Sections 2.7-2.9. Try to do as many of the
exercises in the text as you can. However, turn in only the ones that I assign!
12. Suppose a linear opera
Quantum Mechanics
Problem Set 2
Due: 9 September 2015
Reading: Shankar Sections 1.5-1.8 and 4.2; Lecture notes, Sections 2.5-2.7. Try to do as
many of the exercises in the text as you can. However, turn in only the ones that I assign!
7. Show that both th
Quantum Mechanics
Solution Set 1
Due: 2 September 2015
In this first solution set I give each problem a typical title, as required for full credit.
1. Show that the function (r) = r1 eikr , where r |r|, satisfies the free time independent
3-d Schrodinger
Quantum Mechanics
Problem Set 11
Due: 18 November 2015
Reading: Shankar, Chapter 8 and Lecture Notes, Chapter 8.
57. (Carried over from Set 10). Suppose a simple harmonic oscillator is in an initial state
corresponding to the ground state translated by th
Quantum Mechanics
Problem Set 10
Due: 13 November 2015 (Note that this is a Friday since Wednesday is Veterans day.)
Reading: Chapter 7. Lecture notes, Chapter 7.
53. a) S, Exercise 7.4.2; b) S, Exercise 7.4.3; c) S, Exercise 7.4.6.
54. Suppose a simple h
Quantum Mechanics
Problem Set 8
Due: 28 October 2015
Reading: Shankar, Chapter 5; Lecture notes, Chapter 5 and Sections 6.3-6.4.
41. (Spreading of a Wave Packet). Consider a particle in a state described by the initial
wave function
3/4
1
2
2
er /2x .
r|(
PHY 6645 Fall 2001 Mid-Term Exam 1
Instructions: Attempt both Question 1 (worth 40 points) and Question 2 (worth 60 points).
(Note that Question 2 continues on the back of this page.) The maximum score for each
part of each question is shown in square bra
PHY 6645 Fall 2002 Mid-Term Exam 1
Instructions: Attempt both questions, each of which is worth 50 points. The maximum
score for each part of each question is shown in square brackets. To gain full credit you
should explain your reasoning and show all wor
PHY 6645 Fall 2003 Mid-Term Exam 2
Instructions: Attempt both question 1 (worth 50 points) and question 2 (worth 50 points).
The maximum score for each part of each question is shown in square brackets. To gain
full credit you should explain your reasonin
PHY 6645 Fall 2001 Mid-Term Exam 2
Instructions: Attempt both Question 1 (worth 65 points) and Question 2 (worth 35 points).
The maximum score for each part of each question is shown in square brackets. To gain full
credit you should explain your reasonin
PHY 6645
K. Ingersent
One-Dimensional Wave Mechanics
General arguments and qualitative results will be presented in class concerning solutions
to Schrdingers wave equation for one-dimensional systems. In order to understand and
o
apply this discussion, yo
Quantum Mechanics
Solution Set 4
Due: 24 September 2014
Reading: Shankar Sections 1.8-1.10; Lecture notes, Sections 2.8-2.11. Try to do as many of
the exercises in the text as you can. However, turn in only the ones that I assign!
17. In class we proved t