Phys622: Introduction to Quantum Mechanics I
Fall 1999, Section 0201, MARS #46891
MW 12:00-12:50, F 11-12:50, Room PLS 1140

Instructor: Dr. Ted Jacobson
Room 4117, Phone 301-405-6020,
Office hours: M 10-11, W 2-3

Teaching Assistants:
Hock-Seng Goh  ("Goh") 
Room  4221, Phone 301-405-7279, 
Office hours:  T 10-11, Th1-2 
 Douglas Armstead  ("Doug") 
 Room  4211, Phone 301-405-6192 
 Office hours: W 4-5

General course information

Course content: This is the first semester of a  graduate quantum mechanics course.
Textbook: There is no required textbook for the course, however all students should have at least one standard graduate quantum text on hand. A selection of recommended books is described below.

Reserve books: The books by Baym, Cohen-Tannoudji et. al.,  Landau & Lifshitz,  Sakurai, and Schwabl are (I hope) on reserve at EPSL.
Web pages: Homework assignments and supplementary material at, homework grades and solutions at

E-mail: I encourage students to make use of e-mail for quick correspondence with me regarding lecture material, homework problems, or whatever. I will also use e-mail to communicate with the class at large.

Homework: Assigned weekly and due the following week. Late homework accepted only under dire circumstances. If you know it will be impossible to turn in an assignment on time you must discuss this with me  in advance of the due date. The homework is an essential part of the course. I believe most of what you learn will come from doing the homework. You are encouraged to discuss the homework with others, but what you finally hand in should be your own work.  Sources (e.g. textbooks or classmates) should be cited when used heavily in a homework solution. Please make sure you include your name and the homework and course numbers and staple the pages together.

Exams: Two one-hour mid-terms and a final. The final is Thursday, Dec. 16, 10:30am-12:30pm.

Grading: REVISED: Based on homework (30%), one mid-term (30%), and final (40%),
with the best of  these raised by 20%  and the worst two lowered by 20%.
(Revised since it turned out the homework could all be graded. For the record, the old scheme
was: Based on homework (20%), two mid-terms (20% each), and final (40%), with the best two
of  these raised by 10% each and the worst two lowered by 10% each .)
The lowest two homework scores will be dropped. I cannot say for sure in advance, but I expect the letter grades to correspond to (roughly) (A) 100-80%, (B) 80-60%, (C) 60-40%.

Some texts

F. Schwabl,  Quantum Mechanics
Concise, well-organized, clear exposition.

C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics
Massive, strong on both fundamentals and applications, excellent for self-study.

L.D. Landau and E.M. Lifschitz, Quantum Mechanics (Non-relativistic theory)
Practical and fundamental, with many applications and worked problems.

G. Baym, Lectures on Quantum Mechanics
Informal but sophisticated, very readable, with many applications.

J.J. Sakurai, Modern Quantum Mechanics
Written by a high-energy theorist, tilted toward the algebraic approach. Nice choice of examples.

L.I. Schiff, Quantum Mechanics
A ``standard" old-fashioned graduate textbook. Contains a lot of material and has a good table of contents.

E. Merzbacher, Quantum Mechanics
Another ``standard" graduate text, with the slant of a nuclear theorist. Strong on scattering theory.
A third edition came out in 1997.

H.A. Bethe and R. Jackiw, Intermediate Quantum Mechanics
Atomic structure, interaction with radiation, and scattering theory, beyond the usual introductory topics.

R. Shankar, Principles of Quantum Mechanics
Holds the student's hand, verbose, mostly elementary,  but has some very nice modern applications.

D.J. Griffiths, Introduction to Quantum Mechanics
A very well written modern undergraduate text,  neatly organized and lucid.

P.A.M. Dirac, Principles of Quantum Mechanics
An elegant classic.

R.P. Feynman, The Feynman Lectures on Physics, vol. III
A ``beginning undergraduate" text offering insights that keep professors coming back.

A. Messiah, Quantum Mechanics
Strong on the formal and mathematical aspects of the theory.

J. Preskill, Lecture Notes on Quantum Mechanics and Quantum Computation
Notes from a Cal. Tech. course. Includes a nice introduction to the fundamentals of QM.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions
Indispensable for special functions.

Gradshteyn and Ryzhik: Table of Integrals, Series, and Products
The best.

Topics to be covered

1. inner product spaces, operators, Dirac notation
2. projection operators,  expectation values, structure of QM
3. commuting observables, uncertainty principle
4. combining quantum systems
5. no-cloning, teleportation, non-locality
6. Schrodinger equation
7. canonical quantization
8. position and momentum eigenstates, delta function
9. Heisenberg picture, Ehrenfest's theorem
10. harmonic oscillator, ladder operators, coherent states
11. one dimensional bound states
12. many particles, bosons & fermions
13. Fermi sea
14. Cooper pairs
15. symmetries & conservation laws
16. angular momentum, representation theory, spherical harmonics
17. central potentials
18. Hydrogen atom
19. particle in electromagnetic field, gauge invariance
20. Landau levels
21. Aharonov-Bohm effect, flux quantization, monopoles
22. magnetic moments, Zeeman effect
23. spin-1/2
24. NMR
25. addition of angular momenta, hyperfine interaction, spin-orbit coupling


Calendar (with topics covered, minutes, supplements, & homework)
Class minutes are linked to week numbers in the calendar.

Week  Monday  Wednesday  Friday  HW & Suppts.
1.      8/30 superposition, 
spin-1/2 example, 
qubits & other state spaces
vector spaces, 
linear operators, 
inner product, 
Dirac notation, 
resolution of identity
2.      9/6 no class, Labor Day matrix notation, 
projection operators, 
probability interp.
"collapse" of the state, 
expectation values, 
spectral rep. of observables, 
time evolution, 
composite systems
3.      9/13 entangled states, 
mixed vs. pure states, 
density matrices
commuting observables  position eigenstates, 
translation operator, 
momentum operator
4.       9/20 Schrodinger eqn. in position and momentum representations  computational tricks, 
Ehrenfest's theorem
QM fact sheet 
5.       9/27 general uncertainty reln, 
min. uncert. wavepackets
Heisenberg picture computation tips, 
harmonic oscillator
hw5  (due 10/11)
6.     10/4 coherent states osc. states pos'n rep., 
CUPS simulations
Galilean invariance ``Schrodinger Cat" 
atomic states
7.    10/11 rotations & ang. mom. reps. of rotations spin-1/2, precession, 
Stern-Gerlach expt.
hw6 (due 10/18)
8.     10/18 spin resonance spin resonance, 
central potentials hw7 (due 10/25), 
Rabi on MBMR
9.     10/25 central potentials Coulomb potential, 
Lenz vector & Coulomb potential 
square well levels
10.   11/1 2body ->1body, 
relative ang. mom., 
spin of proton
identical particles composites, 
homonuclear mols., 
Fermi gas
11.   11/8 Fermi sea, 
Cooper pairs
Cooper pairs Cooper pairs, 
charge in magnetic field
Cooper pairs 
12.  11/15 magnetic  field magnetic  moments 
gauge invariance, 
Yang-Mills theory
quantum cyclotron
13.   11/22 gauge invariance, 
Aharonov-Bohm effect
Zeeman effect, 
magnetic monopoles
no class, Thanksgiving .
14.   11/29 flux quantization, 
relativistic effects
spin-orbit coupling, 
Darwin term, 
perturbation theory
fine structure, 
|ljm_j> states
15.   12/6 Lamb shift, 
Zeeman effect
Lamb shift  expt., 
hyperfine interaction
hyperfine splitting, 
16.   12/13 review Final Exam: Thurs. 12/16, 10:30-12:30