Physics 221B
Quantum Mechanics
Spring 2008
University of California, Berkeley
 Instructor: Robert Littlejohn
 Office: 449 Birge
 Office Hours: Thu 34
 Telephone: 6421229
 Email: physics221@wigner.berkeley.edu
TA: Badr Albanna badr@wigner.berkeley.edu
 TA Office Hours: Fri 121; Location: Oppenheimer Room
 Lecture: 247 Cory
 Time: TuTh 89:30
 Discussion Section 1: W 23, 75 Evans
 Discussion Section 2: to be cancelled
 Texts: J. J. Sakurai, Modern Quantum Mechanics,
Revised Edition (AddisonWesley, New York, 1994); J. J. Sakurai, Advanced Quantum Mechanics.

The 221A web site for Fall 2007 is here.
The materials linked to in this web page are out of date.
For current course materials (academic year 20112012),
please look here.
 Final Exam: Wednesday, May 21, 2008, 811am
Organization and Logistics
The email address for this course is physics221@wigner.berkeley.edu.
If you are registered for Physics 221B, you will automatically be on the mailing list. Otherwise, if you wish to be included on the mailing list
for course announcements, homework notices, etc., send an email to
this address with your name. (You don't have to be enrolled.) If you
drop the course or don't want to receive any more announcements, send
an email to this address with a request to be dropped.
The course web
site (this site) will be used to post lecture notes, special
notes, homework assignments, and homework solutions.
I will probably cancel the Tuesday discussion section, and rely on
the Wednesday section plus office hours to cover your needs. I will
schedule my office hour and, if necessary, the discussion section so
the maximum number of students can attend at least one.
I will be out of town the week of March 1721. I will either
have a substitute lecturer that week, or else schedule makeups.
Prerequisites for
this course include graduate standing and Physics 221A or equivalent
course. Students who do not have this background are required to get
instructor's approval before enrolling. In particular, this applies to
all undergraduates
wishing to take the course.
The grade will be
based on homework and the final exam, with some fractions to be
determined. The final exam will either be inclass, takehome, or
oral; I haven't decided which yet, but I will let you know by the
middle of the semester. In the meantime, please keep the inclass
exam time open (plan to be in Berkeley).
Homework policy is the same as last semester.
Weekly homework
assignments will be made available on this web site by Friday
morning of each week, and will be due at 5pm on Friday afternoon of
the following week. Homework should be turned in in the 221B homework
box in 251 LeConte (the reading room).
Late homeworks will
be accepted up to one week late at 50% credit. Homeworks more than one
week late will not be accepted. Please do not ask the reader to take
late homeworks. Exception: Each student is allowed one free late
homework (up to one week late) during the semester, no questions
asked.
Students are encouraged to
work together on homework, and to trade ideas. There is no
better way to learn. However, it is expected that the work you turn is
in your own words and that it reflects your own understanding of the
problem. It is not legal just to copy someone else's solutions. It
is also strictly
illegal to look at or use solutions from any previous version
of this course from earlier years. You can't find those solutions
anyway without going to some extra trouble.
In the first part of 221B we will continue with the text we used
in the fall semester, Modern Quantum
Mechanics, by J. J. Sakurai. Later we will switch to the
second text, Advanced Quantum
Mechanics, also by J. J. Sakurai.
Physics 221B will cover atomic physics, timedependent
perturbation theory and scattering theory, quantization of the
electromagnetic field, and an introduction to relativistic quantum
mechanics including the Dirac equation, first and second quantized.
Lecture notes
will be available in one of two forms. For some lectures I have
typedup notes. There will not be as many of these as there were in
the Fall semester. For those lectures without typed notes, I will
usually try to supply handwritten notes, although I don't guarantee
how closely they will follow the actual lectures. Nevertheless, it
should be possible to get by without taking notes in class. Please do
not be afraid to interrupt the lecture to ask questions in class.
 Tuesday, August 28, 2007: See Notes 1.
 Thursday, August 30, 2007: See Notes 1,2.
 Tuesday, September 4, 2007: See Notes 2,3.
 Thursday, September 6, 2007: See Notes 3,4.
 Tuesday, September 11, 2007: See Notes 4,5.
 Thursday, September 13, 2007: See Notes 5, with extra notes.
 Tuesday, September 19, 2007: See Notes 6.
 Thursday, September 20, 2007: See Notes 6, with extra notes.
 Tuesday, September 25, 2007: See Notes 7.
 Thursday, September 27, 2007: See Notes 7, with extra notes.
 Tuesday, October 16, 2007: See Notes 9,10.
 Thursday, October 18, 2007: See Notes 10,11.
 Tuesday, October 23, 2007: See Notes 11,12.
 Thursday, October 25, 2007: See Notes 12,13.
 Tuesday, November 6, 2007: See Notes 15,16.
 Thursday, November 8, 2007: See Notes 16.
 Tuesday, November 20, 2007: See Notes 18,19.
 Thursday, November 22, 2007: Thanksgiving holiday.
 Tuesday, November 27, 2007: See Notes 19,20.
 Thursday, November 29, 2007: See Notes 20,21.
 Tuesday, December 4, 2007: See Notes 22.
 Thursday, December 6, 2007: See Notes 23, with extra notes.
 Tuesday, January 22, 2008: See Notes 24,25.
 Thursday, January 24, 2008: See Notes 25, with extra notes.
 Tuesday, January 29, 2008: notes and
Notes 26,27.
 Thursday, January 31, 2008: See Notes 27.
 Tuesday, February 5, 2008: See Notes 27,28 with extra notes.
 Thursday, February 7, 2008: notes.
 Tuesday, February 12, 2008: See Notes 29.
 Thursday, February 14, 2008: notes.
 Tuesday, February 19, 2008: notes and more notes.
 Thursday, February 21, 2008: See Notes 31.
 Tuesday, February 26, 2008: notes.
 Thursday, February 28, 2008: See Notes 34.
 Tuesday, March 4, 2008: See Notes 34, 36.
 Thursday, March 6, 2008: See Notes 36.
 Tuesday, March 11, 2008: See Notes 36, 37.
 Thursday, March 13, 2008: See Notes 37.
 Tuesday, March 18, 2008: See Notes 36, 38.
 Thursday, March 20, 2008: notes.
 Tuesday, April 1, 2008: notes.
 Thursday, April 3, 2008: notes.
 Tuesday, April 8, 2008: notes.
 Thursday, April 10, 2008: notes.
 Tuesday, April 15, 2008: notes.
 Thursday, April 17, 2008: notes.
 Tuesday, April 22, 2008: notes.
 Thursday, April 24, 2008: See Chapter 3 of Bjorken
and Drell.
 Tuesday, April 29, 2008: See Chapter 4 of Bjorken
and Drell.
 Thursday, May 1, 2008: notes.
 Tuesday, May 6, 2008: notes.
 Tuursday, May 8, 2008: notes.
Homework
assignments
will normally be made available on this web site by Friday of
each week, and will be due at 5pm on Friday of the following week in
the 221B homework box in 251 LeConte (the reading room).
 Homework 1, due Thursday, September 6 at 5pm, in postscript or pdf
format.
 Homework 2, due Thursday, September 13 at 5pm, in postscript or pdf
format.
 Homework 3, due Thursday, September 20 at 5pm, in postscript or pdf
format.
 Homework 4, due Friday, September 28 at 5pm, in postscript or pdf
format.
 Homework 5, due Friday, October 5 at 5pm, in postscript or pdf
format.
 Homework 6, due Friday, October 12 at 5pm, in postscript or pdf
format.
 Homework 7, due Friday, October 19 at 5pm, in postscript or pdf
format.
 Homework 8, due Friday, October 26 at 5pm, in postscript or pdf
format.
 Homework 9, due Friday, November 2 at 5pm, in postscript or pdf
format.
 Homework 10, due Friday, November 9 at 5pm, in postscript or pdf
format.
 Homework 11, due Friday, November 16 at 5pm, in postscript or pdf
format.
 Homework 12, due Monday, November 26 at 5pm, in postscript or pdf
format.
 Homework 13, due Friday, November 30 at 5pm, in postscript or pdf
format.
 Homework 14, due Monday, December 10 at 5pm, in postscript or pdf
format.
 Homework 15, due Friday, January 25 at 5pm, in postscript or pdf
format.
 Homework 16, due Friday, February 1 at 5pm, in postscript or pdf
format.
 Homework 17, due Friday, February 8 at 5pm, in postscript or pdf
format.
 Homework 18, due Friday, February 15 at 5pm, in postscript or pdf
format.
 Homework 19, due Friday, February 22 at 5pm, in postscript or pdf
format.
 Unhomework 20, nothing due, in postscript or pdf
format.
 Homework 21, due Friday, March 7 at 5pm, in postscript or pdf
format.
 Homework 22, due Friday, March 14 at 5pm, in postscript or pdf
format.
 Homework 23, due Monday, March 31 at 5pm, in postscript or pdf
format.
 Homework 24, due Friday, April 4 at 5pm, in postscript or pdf
format.
 Homework 25, due Friday, April 18 at 5pm, in postscript or pdf
format.
 Homework 26, due Friday, April 25 at 5pm, in postscript or pdf
format.
 Homework 27, due Friday, May 2 at 5pm, in postscript or pdf
format.
 Homework 28, due Friday, May 9 at 5pm, in postscript or pdf
format.
 Homework 29, due Friday, May 16 at 5pm, in postscript or pdf
format.
Typed lecture
notes are available for some lectures, not others. (These notes
have been updated somewhat since the end of the 0708 academic year. See the 20112012 course web site for the most uptodate set of notes.)
 Notes 1: The Mathematical
Formalism of Quantum Mechanics, in
ps or
pdf
format.
 Notes 2: The Postulates of
Quantum Mechanics, in ps or
pdf format (complete).
 Notes 3: The Density
Operator, in ps or
pdf format.
 Notes 4: Spatial Degrees of
Freedom, in ps or
pdf format (complete).
 Notes 5: Time Evolution in
Quantum Mechanics, in ps or
pdf format.
 Notes 6: Topics in OneDimensional
Wave Mechanics, in ps or
pdf format.
 Notes 7: The WKB Method,
in ps or
pdf format.
 Notes 8: Harmonic Oscillators
and Coherent States,
in ps or
pdf format.
 Notes 9: The Propagator and
the Path Integral, in ps or
pdf format.
 Notes 10: Charged Particles in
Magnetic Fields, in ps or
pdf format.
 Notes 11: Rotations in Ordinary
Space, in ps or
pdf format (complete).
 Notes 12: Rotations in Quantum
Mechanics, and Rotations of Spin 1/2 Systems, in
ps or
pdf format.
 Notes 13: Representations of
the Angular Momentum Operators and Rotations, in
ps or
pdf format.
 Notes 14: Spins in Magnetic
Fields, in ps or
pdf format (complete).
 Notes 15: Orbital Angular
Momentum and Spherical Harmonics, in ps or pdf format (complete).
 Notes 16: Central Force
Motion, in ps or pdf format.
 Notes 17: Coupling of Angular
Momenta, in ps or pdf format.
 Notes 18: Irreducible Tensor
Operators and the WignerEckart Theorem, in ps or pdf
format.
 Notes 19: Parity, in ps or pdf
format.
 Notes 20: Time Reversal, in ps or pdf
format (complete).
 Notes 21: BoundState Perturbation
Theory, in ps or pdf format.
 Notes 22: The Stark Effect in Hydrogen
and Alkali Atoms, in ps or pdf format.
 Notes 23: Fine Structure in Hydrogen
and Alkali Atoms, in ps or pdf format.
 Notes 24: The Zeeman Effect in Hydrogen
and Alkali Atoms, in ps or pdf format.
 Notes 25: Hyperfine Structure in
Hydrogen, in ps or pdf format.
 Notes 26: Identical Particles,
in ps or pdf format.
 Notes 27: Helium and Heliumlike
Atoms, in ps or pdf format.
 Notes 28: The ThomasFermi Model,
in ps or pdf format.
 Notes 29: The HartreeFock Method in
Atoms, in ps or pdf format (complete).
 Notes 30: Elements of Atomic Structure
in MultiElectron Atoms, in ps or pdf format.
 Notes 31: TimeDependent Perturbation
Theory, in ps or pdf format.
 Notes 32: The Photoelectric
Effect, in ps or pdf format.
 Notes 33: Green's Functions in
Quantum Mechanics, in
ps or pdf format.
 Notes 34: The LippmannSchwinger
Equation, in ps or pdf format.
 Notes 35: Adiabatic Invariance,
the Geometric Phase, and the BornOppenheimer Approximation,
in ps or pdf format.
 Notes 36: The Classical
Electromagnetic Field Hamiltonian, in ps or pdf
format (complete).
 Notes 37: Lagrangian and
Hamiltonian Formulation of the Classical Electromagnetic Field, in ps or pdf
format.
 Notes 38: The Quantized
Electromagnetic Field, in ps or pdf
format.
 Notes 39: Interaction of Radiation
with Matter, in ps or
pdf format.
 Notes 40: Scattering of Radiation
by Matter, in ps or
pdf format.
 Appendix A: Gaussian, SI and
Other Systems of Units in Electromagnetic Theory, in ps or pdf format.
 Appendix B: Classical
Mechanics, in ps or pdf format.
Homework Solutions.
Reprints.
 I can do that for you! in
pdf format only.
 History of the Lamb shift,
in pdf format only.
 Covariance of the Dirac Equation, in pdf format only.
 Solutions of the Dirac Equation for a Free Particle, in pdf format only.
 The FoldyWouthuysen Transformation, in pdf format only.
Extra Notes.
 Notes on Variational Principles
in Classical Mechanics in ps or
pdf format.
 Table of ClebschGordan
Coefficients, etc in pdf
format only.
 Notes on Thomas Precession,
in ps or pdf format.