Physics 221B
Quantum Mechanics
Spring 2011
University of California, Berkeley
- Instructor: Robert Littlejohn
- Office: 449 Birge
- Office Hours: Friday 12-1
- Telephone: 642-1229
- Email: physics221@wigner.berkeley.edu
TA: Austin Hedeman, Office Hours Thursday 2-3, Room 432 Birge austin@wigner.berkeley.edu
-
- Lecture: 9 Lewis
- Time: MWF 9-10
- Discussion Section 1: cancelled
- Discussion Section 2: Th 3-4, 105 Latimer
- Recommended text: J. J. Sakurai, Advanced Quantum Mechanics.
-
The 221A web site for Fall 2010 is here.
The materials linked to in this web page are out of date.
For current course materials (academic year 2011-2012),
please look here.
- Final Exam: Monday, May 9, 7-10pm
- Location: TBA
Organization and Logistics
The email address for this course is physics221@wigner.berkeley.edu. Use
this to send me emails if you have any questions etc. Also, I
maintain an email mailing list for the course, and use it to send out
announcements, corrections to homework assignments, etc back to you.
If you were on the email list last semester, you will continue to be
on it this semester. If you 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.
Discussion section time and office hour will remain as they were
last semester.
Prerequisites for
this course include Physics 221A or equivalent. 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 a final exam. I may decide to give an oral
final exam instead of a written one, or not to give a final at all. I
will let you know by roughly the middle of the semester.
Weekly homework
assignments will be made available on this web site (usually)
by Friday or Saturday of each week, and will be due at 5pm on Friday
afternoon of the following week. Homework should be turned in in the
221A homework box in 251 LeConte (the reading room). This is the same
policy as last semester.
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 in
is your own work in your own words. 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 trouble.
The text for the course, Modern
Quantum Mechanics, by J. J. Sakurai, was chosen because of its
good selection of topics and because of the generally deep perspective
it takes in developing the subject. Unfortunately, the explanations in
the book are often poor and sometimes wrong; this seems to be due to
the fact that Sakurai died before he could put his book into
order. (His other book, Advanced
Quantum Mechanics, which we will use in Physics 221B, is much
better.) To make up for these deficiencies, most weeks there will be
lecture notes made available which will supplement the readings from
the text.
The content of Physics 221A is mostly a review of undergraduate
quantum mechanics, presented from a deeper point of view and with a
different emphasis. Some new topics are also presented. Physics 221B
presents much new material, including an introduction to field theory
and relativistic quantum mechanics. The course will have an emphasis
on atomic physics that gradually turns into particle physics.
Lecture notes
will be available in one of two forms. For some lectures I have
typed-up notes. For those lectures without typed notes, I will usually
try to supply hand-written 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. Do not be afraid
to interrupt the lecture to ask questions.
Unfortunately, Daniel and Greg are no longer available to take
videos of the lectures, so there will be no videos this semester.
- Friday, August 27, 2010: Notes 1, pp. 1-13. See also the
video. On looking at
this video, I see that the web address I put on the board for
this web site was wrong. But there is no point in correcting
it, since you wouldn't be here if you had the wrong address.
`
- Monday, August 30, 2010: Notes 1, pp. 13-25. See also the
video.
- Wednesday, September 1, 2010: Notes 1, pp. 25-31,
Notes 2, pp. 1-7. See also the
video.
- Friday, September 3, 2010: Notes 2, pp. 7-14,
Notes 3, pp. 1-11. See also the
video.
- Tuesday, September 7, 2010: Notes 3, pp. 11-18, Notes 4,
pp. 1-4. See also the video.
- Wednesday, September 8, 2010: Notes 4, pp. 4-17. See also the
video.
- Friday, September 10, 2010: Notes 5, pp. 1-15. See also the video.
- Monday, September 13, 2010: Notes 5, pp. 15-19, Notes 6,
pp. 1-4, Notes 7, pp. 1-5. See also the video.
- Wednesday, September 15, 2010: Notes 7, pp. 5-16. See also the
video.
- Friday, September 17, 2010: Notes 7, pp. 16-25. See also the
video.
- Monday, September 20, 2010: Notes 7, pp. 25-26, extra notes, and Notes 8,
pp. 1-7. See also the video.
- Wednesday, September 22, 2010: Notes 8, pp. 7-15. See also the
video.
- Friday, September 24, 2010: No lecture.
- Monday, September 27, 2010: Notes 8, pp. 15-17, Notes 9,
pp. 1-8. See also the video.
- Wednesday, September 29, 2010: Notes 9, pp. 8-19. See also the
video.
- Friday, October 1, 2010: Notes 9, pp. 19-24. See also the
video.
- Monday, October 4, 2010: Notes 9, pp. 25-27, Notes 10,
pp. 1-6. See also the
video.
- Tuesday, October 5, 2010: Notes 10, pp. 6-10 and extra notes. See also the
video.
- Friday, October 7, 2010: No lecture.
- Monday, October 11, 2010: Notes 10, pp. 10-12, Notes 11,
pp. 1-5 and extra notes. See also the
video.
- Wednesday, October 13, 2010: Notes 11, pp. 6-15, Notes 12,
pp. 1-3. See also the
video.
- Friday, October 15, 2010: Notes 12, pp. 3-12. See also the
video.
- Monday, October 18, 2010: Notes 12, pp. 12-16; Notes 13,
pp. 1-9. See also the
video.
- Wednesday, October 20, 2010: Notes 13, pp. 9-13; Notes
14, pp. 1-4. See also the
video.
- Friday, October 22, 2010: Notes 14, pp. 4-14. See also the
video.
- Monday, October 25, 2010: Notes 14, pp. 14--18, Notes 15,
pp. 1--7. See also the
video.
- Wednesday, October 27, 2010: Notes 15, pp. 7--12, Notes 16,
pp. 1--6. See also the
video.
- Friday, October 29, 2010: Notes 16, pp. 7--13, and extra notes. See also the
video.
- Monday, November 1, 2010: extra notes on hydrogen.
See also the video.
- Wednesday, November 3, 2010: extra notes on coupling
spatial and spin degrees of freedom.. Also, Notes 17,
pp. 1-5, and Sec. 3 of Notes 23 on the spin-orbit term.
See also the video.
- Friday, November 5, 2010: Notes 17, pp. 5-12, Notes 18, p. 1.
See also the video.
- Monday, November 8, 2010: Notes 18, pp. 1-11. See also
the video.
- Wednesday, November 10, 2010: Notes 18, pp. 11-20. See
also the video.
- Friday, November 12, 2010: Notes 18, pp. 20-24, Notes 19,
pp. 1-5. See also the video
.
- Monday, November 15, 2010: Notes 19, pp. 5-11, Notes 20,
pp. 1-2. See also the
video.
- Wednesday, November 17, 2010: Notes 20, pp. 2-10. See
also the video.
- Friday, November 19, 2010: Notes 20, pp. 11-18. See
also the video.
- Monday, November 22, 2010: Notes 21, entire. See
also the video.
- Tuesday, November 23, 2010: Notes 22, pp. 1-12. See
also the video.
- Wednesday, November 24, 2010: Notes 22, pp. 13-14, Notes 23,
pp. 1-5. See also the video.
- Monday, November 29, 2010: Notes 23, pp. 5-12, Notes 24, pp. 1-3.
See also the video.
- Wednesday, December 1, 2010: Notes 24, pp. 3--8. See also the
video.
- Monday, December 6, 2010: No notes, lecture on deuteron. See
also the video.
- Wednesday, January 19, 2011: Notes 25, pp.~1-7.
- Friday, January 21, 2011: Notes 25, pp. 7-11; Notes 26, pp. 1-4.
- Monday, January 24, 2011: Notes 26, pp. 4-6; Notes 27, pp. 1-10.
- Wednesday, January 26, 2011: Notes 27, pp. 10-13, Notes 28,
pp. 1-4.
- Friday, January 28, 2011: Notes 28, pp. 4-11.
- Monday, January 31, 2011: Notes 28, pp. 11-17.
- Wednesday, February 2, 2011: extra notes on helium.
- Friday, February 4, 2011: Notes 30, pp. 1-8.
- Monday, February 7, 2011: Notes 30, pp. 8-15.
- Wednesday, February 9, 2011: Notes 30, pp. 15-21.
- Friday, February 11, 2011: Notes 30, pp. 21-27, Notes 31, pp.
1-5.
- Monday, February 14, 2011: Notes 31, pp. 5-6, extra notes on atomic
structure.
- Wednesday, February 16, 2011: more notes on atomic
structure, Notes 32, pp. 1-3.
- Friday, February 18, 2011: Notes 32, pp. 3-11.
- Monday, February 21, 2011: Holiday, no lecture.
- Wednesday, February 23, 2011: Notes 32, pp. 11-18, Notes
37, pp. 1-6.
- Friday, February 25, 2011: Notes 37, pp. 6-13.
- Monday, Februrary 28, 2011: Notes 37, pp. 13-21.
- Wednesday, March 2, 2011: Notes 37, pp. 21-26.
- Friday, March 4, 2011: Notes 37, pp 26-27, Notes 39, pp. 1-3.
- Monday, March 6, 2011: Notes 39, pp. 3-8.
- Wednesday, March 8, 2011: Notes 39, pp. 8-16.
- Friday, March 10, 2011: Notes 39, pp. 16-17, Notes 40,
pp. 1-5.
- Monday, March 13, 2011: Notes 40, pp. 5-10.
- Wednesday, March 15, 2011: Notes 40, pp. 10-15.
- Friday, March 17, 2011: Notes 40, pp. 15-18, and more notes, pp. 1-5.
- Monday, March 28, 2011: Handwritten notes, pp. 5-17.
- Wednesday, March 30, 2011:Handwritten notes, p. 18
and more notes, pp. 1-8.
- Friday, April 1, 2011:Handwritten notes, pp.
8-21.
- Monday, April 4, 2011:Handwritten notes, p. 22,
and more notes, pp. 1-10.
- Wednesday, April 6, 2011:Handwritten notes, pp. 11-20.
- Friday, April 8, 2011:Handwritten notes, pp. 21--23,
and more notes, pp. 1-10.
- Monday, April 11, 2011:Handwritten notes, pp.10--18,
also Bjorken and Drell, Chapter 2.
- Wednesday, April 13, 2011: Bjorken and Drell, Chapter 2.
- Friday, April 15, 2011: Bjorken and Drell, Chapter 3.
- Monday, April 18, 2011: Bjorken and Drell, Chapters 3,4.
- Wednesday, April 20, 2011: Bjorken and Drell, Chapter 4, and
Handwritten notes.
- Friday, April 22, 2011:
Handwritten notes on the second quantization of the Dirac field, and
more notes, pp. 1-5.
Homework
assignments
will normally be made available on this web site by Friday or Saturday of
each week, and will be due at 5pm on Friday of the following week in
the 221A homework box in 251 LeConte (the reading room).
- Homework 1, due Friday, September 3 at 5pm, in postscript or pdf
format.
- Homework 2, due Friday, September 10 at 5pm, in postscript or pdf
format.
- Homework 3, due Friday, September 17 at 5pm, in postscript or pdf
format.
- Homework 4, due Friday, September 24 at 5pm, in postscript or pdf
format.
- Homework 5, due Friday, October 1 at 5pm, in postscript or pdf
format.
- Homework 6, due Friday, October 8 at 5pm, in postscript or pdf
format.
- Homework 7, due Friday, October 15 at 5pm, in postscript or pdf
format.
- Homework 8, due Friday, October 22 at 5pm, in postscript or pdf
format.
- Homework 9, due Friday, October 29 at 5pm, in postscript or pdf
format.
- Homework 10, due Friday, November 5 at 5pm, in postscript or pdf
format.
- Homework 11, due Friday, November 12 at 5pm, in postscript or pdf
format.
- Homework 12, due Friday, November 19 at 5pm, in postscript or pdf
format.
- Homework 13, due Monday, November 29 at 5pm, in postscript or pdf
format.
- Homework 14, due Friday, December 3 at 5pm, in postscript or pdf
format.
- Homework 15, due Friday, December 10 at 5pm, in postscript or pdf
format.
- Homework 16, due Friday, January 28 at 5pm, in postscript or pdf
format.
- Homework 17, due Friday, February 4 at 5pm, in postscript or pdf
format.
- Homework 18, due Friday, February 11 at 5pm, in postscript or pdf
format.
- Homework 19, due Friday, February 18 at 5pm, in postscript or pdf
format.
- Homework 20, due Friday, February 25 at 5pm, in postscript or pdf
format.
- Homework 21, due Friday, March 4 at 5pm, in postscript or pdf
format.
- Homework 22, due Friday, March 11 at 5pm, in postscript or pdf
format.
- Homework 23, due Friday, March 18 at 5pm, in postscript or pdf
format.
- Homework 24, due Friday, April 1 at 5pm, in postscript or pdf
format.
- Homework 25, due Friday, April 8 at 5pm, in postscript or pdf
format.
- Homework 26, due Friday, April 15 at 5pm, in postscript or pdf
format.
- Homework 27, due Friday, April 22 at 5pm, in postscript or pdf
format.
- Homework 28, due Friday, April 29 at 5pm, in postscript or pdf
format.
Typed lecture
notes are available for some lectures, not others.
- Notes 1: The Mathematical
Formalism of Quantum Mechanics, in
ps or
pdf
format (complete).
- Notes 2: The Postulates of
Quantum Mechanics, in ps or
pdf format (complete).
- Notes 3: The Density
Operator, in ps or
pdf format (complete).
- Notes 4: Spatial Degrees of
Freedom, in ps or
pdf format (complete).
- Notes 5: Time Evolution in
Quantum Mechanics, in ps or
pdf format (complete).
- Notes 6: Topics in
One-Dimensional Wave Mechanics, in ps or
pdf format (complete).
- Notes 7: The WKB Method,
in ps or
pdf format (complete).
- Notes 8: Harmonic Oscillators
and Coherent States,
in ps or
pdf format (complete).
- Notes 9: The Propagator and
the Path Integral, in ps or
pdf format (complete).
- Notes 10: Charged Particles in
Magnetic Fields, in ps or
pdf format (complete).
- 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 (complete).
- Notes 13: Representations of
the Angular Momentum Operators and Rotations, in
ps or
pdf format (complete).
- 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 (complete).
- Notes 17: Coupling of Angular
Momenta, in ps or pdf format (complete).
- Notes 18: Irreducible Tensor
Operators and the Wigner-Eckart Theorem, in ps or pdf
format (complete).
- Notes 19: Parity, in ps or pdf
format (complete).
- Notes 20: Time Reversal, in ps or pdf
format.
- Notes 21: Bound-State 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
Atoms, in ps or pdf format.
- Notes 26: The Variational
Method, in ps or pdf format.
- Notes 27: Identical Particles,
in ps or pdf format.
- Notes 28: Helium and Helium-like
Atoms, in ps or pdf format.
- Notes 29: The Thomas-Fermi Model,
in ps or pdf format.
- Notes 30: The Hartree-Fock Method in
Atoms, in ps or pdf format.
- Notes 31: Elements of Atomic Structure
in Multi-Electron Atoms, in ps or pdf format.
- Notes 32: Time-Dependent Perturbation
Theory, in ps or pdf format.
- Notes 33: The Photoelectric
Effect, in ps or pdf format.
- Notes 34: Green's Functions in
Quantum Mechanics, in
ps or pdf format.
- Notes 35: The Lippmann-Schwinger
Equation, in ps or pdf format.
- Notes 36: Adiabatic Invariance,
the Geometric Phase, and the Born-Oppenheimer Approximation,
in ps or pdf format.
- Notes 37: The Classical
Electromagnetic Field Hamiltonian, in ps or pdf
format.
- Notes 38: Lagrangian and
Hamiltonian Formulation of the Classical Electromagnetic Field, in ps or pdf
format.
- Notes 39: The Quantized
Electromagnetic Field, in ps or pdf
format.
- Notes 40: Interaction of Radiation
with 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.
- Appendix C: Gaussian
Integrals, in ps or pdf format (incomplete).
Homework Solutions for Fall 2010 and
Spring 2011.
Reprints.
- Feynman and Hibbs, Chapter 1 in
pdf format only.
- I can do that for you! in
pdf format only.
- Table of Clebsch-Gordan
Coefficients, etc in pdf
format only.
- Handwritten notes and
more notes on central force
scattering.
- Bjorken and Drell, Chapter 2 in
pdf format only.
- Bjorken and Drell, Chapter 3 in
pdf format only.
- Bjorken and Drell, Chapter 4 in
pdf format only.
Exams.
- Spring 2011 final exam in
ps and pdf formats.