Instructor: Dr. Ted Jacobson
Room 4117, Phone 301-405-6020
Office hours: M 10-11, W 2-3
|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
Web pages: Homework assignments and supplementary material at www.glue.umd.edu/~tajac/622c/, homework grades and solutions at http://www.glue.umd.edu/~hsgoh/.
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%.
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
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
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
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.|
qubits & other state spaces
resolution of identity
|2. 9/6||no class, Labor Day||matrix notation,
|"collapse" of the state,
spectral rep. of observables,
EPR & GHZ I
|3. 9/13||entangled states,
mixed vs. pure states,
|commuting observables||position eigenstates,
|4. 9/20||Schrodinger eqn. in position and momentum representations||computational tricks,
EPR & GHZ II
QM fact sheet
|5. 9/27||general uncertainty reln,
min. uncert. wavepackets
|Heisenberg picture||computation tips,
|hw5 (due 10/11)|
|6. 10/4||coherent states||osc. states pos'n rep.,
|7. 10/11||rotations & ang. mom.||reps. of rotations||spin-1/2, precession,
|hw6 (due 10/18)|
|8. 10/18||spin resonance||spin resonance,
MBMR, NMR, MRI
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
|11. 11/8||Fermi sea,
|Cooper pairs||Cooper pairs,
charge in magnetic field
|12. 11/15||magnetic field||magnetic moments
|13. 11/22||gauge invariance,
|no class, Thanksgiving||.|
|14. 11/29||flux quantization,
|15. 12/6||Lamb shift,
|Lamb shift expt.,
|16. 12/13||review||Final Exam: Thurs. 12/16, 10:30-12:30|