Physics 221AB
Quantum Mechanics
Fall 2019 and Spring 2020
University of California, Berkeley
- Instructor: Robert Littlejohn
- Office: 449 Birge
- Office Hours: Fridays 11am-12
- Telephone: 642-1229
- Email: physics221@wigner.berkeley.edu
TA: David Dunsky
Office Hours: Thursdays, 10-11am, Panic Room (4th Floor Birge)
-
- Lecture: 251 LeConte
- Time: TuTh 6:30-8pm
- Discussion Section 101: Wed 4-5, 205 Dwinelle
- Discussion Section 102: Tue 11-12,
310 Hearst Mining
- Recommended text: Eugene D. Commins, Quantum Mechanics: An Experimentalist's Approach.
-
- Final Exam: Take Home; Available 5pm Tuesday,
May 12; due 5pm Thursday, May 14. Link to Final Exam
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 received an email from me on Wednesday, January 15, 2020, then
you are on the email mailing list and do not need to do anything. If
you did not receive an email from me, then send an email to the course
email address (above) and ask to be added to the mailing list (you do
not need 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.
There will be no discussion section during the first week.
The prerequisites for
221B are graduate standing and Physics 221A or equivalent. "Graduate
standing" implies a graduate student in the physics department, so it
will be expected that you have sufficient background in subjects such
as classical mechanics, statistical mechanics and electricity and
magnetism to do this course. Note that this course also requires a
background in special relativity, such as what is taught in Physics
209. Graduate students from other departments are advised that some
knowledge of these subjects will be required for Physics 221B.
Undergraduates wishing to take this course must make an application by
filling out a form that may be obtained from Kathy Lee in the student
services offices. The instructor will review these forms and decide
on the admission of all undergraduate applicants. To be accepted you
must have completed Physics 221A or equivalent, and you must also have
had a sufficient number of other upper division physics courses, and
you must have done well in all of them.
The grade will be
based on homework and a final exam. The final exam will be a
take-home; details will be announced later, but I expect it to be
similar to a homework assignment, except that it will attempt to cover
the whole course.
Weekly homework
assignments will be made available on this web site (usually)
by Saturday 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 on the second floor of LeConte at the entrance to the
breezeway that crosses over to Birge Hall.
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.
Lecture notes
will be available in one of two forms. By now typed up versions of
lecture notes are available for almost all my lectures, but for those
lectures without typed notes, I will usually try to supply
hand-written notes. There are enough notes that usually it should be
possible to get by without taking notes in class. Do not be afraid to
interrupt the lecture to ask questions.
- Thursday, August 29, 2019: Notes 1, Secs. 1-18.
- Tuesday, September 3, 2019: Notes 1, Secs. 19-28; Notes 2,
Secs. 1-2.
- Thursday, September 5, 2019: Notes 2, Secs. 3-9; Notes 3,
Secs. 1-6.
- Tuesday, September 10, 2019: Note 3, Secs. 7-19; Notes 4,
Secs. 1-9.
- Thursday, September 12, 2019: Notes 4, Secs. 10-18; Notes 5,
Secs. 1-15.
- Tuesday, September 17, 2019: Notes 5, Secs. 16-18; Notes 6,
entire; Notes 7, Secs. 1--5.
- Thursday, September 19, 2019: Notes 7, Secs. 6-11.
- Tuesday, September 24, 2019: Notes 7, Secs. 12-13, Notes 8,
Secs. 1-8.
- Thursday, September 26, 2019: Notes 8, Secs. 9-10; Notes 9,
Secs. 1-4.
- Tuesday, October 1, 2019: Notes 9, Secs. 5-9, 11-13, 16-17.
- Thursday, October 3, 2019: Notes 9, Sec. 18; Notes 10, Secs.
1-4.
- Tuesday, October 8, 2019: Notes 10, Secs. 5-7.
- Thursday, October 10, 2019: Power out.
- Tuesday, Ocober 15, 2019: Note 11, Secs.1-13.
- Thursday, October 17, 2019: Notes 12, Secs. 1-11 and 13-14;
Notes 13, Sec. 1.
- Tuesday, October 22, 2019: Notes 13, Secs. 2-10.
- Thursday, October 24, 2019: Notes 13, Sec. 11, Notes 14,
Secs. 1-7.
- Tuesday, October 29, 2019: Notes 14, Secs. 8-9; Notes 15,
Secs. 1-6.
- Wednesday, October 30, 2019: Notes 15, Secs. 6-12; Notes 16,
Secs. 1-5.
- Thursday, October 31, 2019: Notes 16, Secs. 6-11, Notes 17,
Secs 1-4.
- Tuesday, Novenber 5, 2019: Notes 17, Secs. 5-10; Notes 18,
Secs. 1-9.
- Thursday, November 7, 2019: Notes 18, Secs. 10-15; Notes 19,
Secs. 1-6.
- Tuesday, November 12, 2019: Notes 19, Secs. 7-16.
- Thursday, November 14, 2019: Notes 19, Secs. 17-19; Notes 20,
Secs. 1-7.
- Tuesday, November 19, 2019: Notes 20, Secs. 8-11, Notes 21,
Secs. 1-15.
- Thursday, November 21, 2019: Notes 21, Secs. 16-19; Notes 22,
entire; Notes 23, Secs. 1-9.
- Tuesday, November 26, 2019: Notes 23, Secs. 10-16; Notes 24,
Secs. 1-7.
- Tuesday, December 3, 2019: Notes 24, Secs. 8-18.
- Thursday, December 5, 2019: Notes 25, entire; Notes 26,
Secs. 1-3.
- Tuesday, January 21, 2020: Notes 26, Secs. 4-8.
- Thursday, January 23, 2020: Notes 27, entire; Notes 28,
Secs. 1-5.
- Tuesday, January 28, 2020: Notes 28, Secs. 6-8; Notes 29,
Secs. 1-5.
- Wednesday, January 29, 2020: Notes 29, Secs. 6-10.
- Tuesday, February 4, 2020: Notes 29, Secs. 11-12; Notes 31,
Secs. 1-4.
- Thursday, February 6, 2020: Notes 31, Secs. 5-12.
- Tuesday, February 11, 2020: Notes 31, Secs. 13-14, 16.
- Thursday, February 13, 2020: Notes 32 entire.
- Tuesday, February 18, 2020: Notes 33, Secs. 1-11.
- Thursday, February 20, 2020: Notes 33, Secs. 12-21; Notes 35,
Secs. 1-3.
- Tuesday, February 25, 2020: Notes 35, Secs. 4-9.
- Thursday, February 27, 2020: Notes 35, Secs, 10-14; Notes
36, Secs. 1-5.
- Tuesday, March 3, 2020: Notes 36, Secs. 6-18.
- Thursday, March 5, 2020: Notes 37, entire.
- Tuesday, March 10,2020: Notes 39, Secs. 1-14.
- Thursday, March 12, 2020: Notes 39, Secs. 15-20; Notes
40, Secs. 1-3.
- Tuesday, March 31, 2020: Notes 40, Secs. 4-11.
- Thursday, April 2, 2020: Notes 40, Secs. 12-15, 17-21.
- Tuesday, April 7, 2020: Notes 41, Secs. 1-7.
- Thursday, April 9, 2020: Notes 41, Secs. 8-12.
- Tuesday, April 14, 2020: Notes 42, Secs. 1-10.
- Wednesday, April 15, 2020: Notes 42, Secs. 11-14; Notes
43, Sec. 1.
- Thursday, April 16, 2020: Notes 43, Sec. 12; Notes 44,
entire.
- Tuesday, April 21, 2020: Notes 45, entire.
- Wednesday, April 22, 2020: Notes 46, entire.
- Thursday, April 23, 2020: Notes 47, Secs. 1-11.
- Tuesday, April 28, 2020: Notes 47, Secs. 12-17; Notes
48, Secs. 1-6.
- Thursday, April 30, 2020: Notes 48, Secs. 7-10; Notes
49, Secs. 1-7.
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 on the second floor of
LeConte at the entrance to the breezeway that crosses over to Birge
Hall.
- Homework 1, due Friday, September 6 at 5pm, in pdf format.
- Homework 2, due Friday, September 13 at 5pm, in pdf format.
- Homework 3, due Friday, September 20 at 5pm, in pdf format.
- Homework 4, due Friday, September 27 at 5pm, in pdf format.
- Homework 5, due Friday, October 4 at 5pm, in pdf format.
- Homework 6, due Monday, October 14 at 5pm, in pdf format.
- Homework 7, due Friday, October 18 at 5pm, in pdf format.
- Homework 8, due Friday, October 25 at 5pm, in pdf format.
- Homework 9, due Friday, November 1 at 5pm, in pdf format.
- Homework 10, due Friday, November 8 at 5pm, in pdf format.
- Homework 11, due Friday, November 15 at 5pm, in pdf format.
- Homework 12, due Friday, November 22 at 5pm, in pdf format.
- Homework 13, due Monday, December 2 at 5pm, in pdf format.
- Homework 14, due Friday, December 13 at 5pm, in pdf format.
- Homework 15, due Friday, January 31 at 5pm, in pdf format.
- Homework 16, due Friday, February 7 at 5pm, in pdf format.
- Homework 17, due Friday, February 14 at 5pm, in pdf format.
- Homework 18, due Friday, February 21 at 5pm, in pdf format.
- Homework 19, due Friday, February 28 at 5pm, in pdf format.
- Homework 20, due Friday, March 6 at 5pm, in pdf format.
- Homework 21, due Friday, March 13 at 5pm, in pdf format.
- Homework 22, due Friday, April 3 at 5pm, in pdf format.
- Homework 23, due Friday, April 10 at 5pm, in pdf format.
- Homework 24, due Friday, April 17 at 5pm, in pdf format.
- Homework 25, due Friday, April 24 at 5pm, in pdf format.
- Homework 26, due Friday, May 1 at 5pm, in pdf format.
- Unhomework 27, nothing due, in pdf format.
Interesting Movies.
Typed lecture
notes are available for some lectures, not others.
- Notes 1: The Mathematical
Formalism of Quantum Mechanics,
pdf format.
- Notes 2: The Postulates of
Quantum Mechanics, pdf
format.
- Notes 3: The Density
Operator, pdf format.
- Notes 4: Spatial Degrees of
Freedom,
pdf format.
- Notes 5: Time Evolution in
Quantum Mechanics,
pdf format.
- Notes 6: Topics in
One-Dimensional Wave Mechanics,
pdf format.
- Notes 7: The WKB Method,
pdf format.
- Notes 8: Harmonic Oscillators
and Coherent States,
pdf format.
- Notes 9: The Propagator and
the Path Integral,
pdf format.
- Notes 10: Charged Particles in
Magnetic Fields,
pdf format.
- Notes 11: Rotations in
3-Dimensional Space,
pdf format.
- Notes 12: Rotations in Quantum
Mechanics, and Rotations of Spin 1/2 Systems,
pdf format.
- Notes 13: Representations of
the Angular Momentum Operators and Rotations,
pdf format.
- Notes 14: Spins in Magnetic
Fields,
pdf format.
- Notes 15: Orbital Angular
Momentum and Spherical Harmonics, pdf format.
- Notes 16: Central Force
Motion, pdf format.
- Notes 17: Hydrogen, pdf format.
- Notes 18: Coupling of Angular
Momenta, pdf format.
- Notes 19: Irreducible Tensor
Operators and the Wigner-Eckart Theorem, pdf format.
- Notes 20: Parity, pdf format.
- Notes 21: Time Reversal,
pdf format.
- Notes 22: Bound-State Perturbation
Theory, pdf format.
- Notes 23: The Stark Effect in
Hydrogen and Alkali Atoms, in pdf
format.
- Notes 24: Fine Structure in
Hydrogen and Alkali Atoms, pdf format.
- Notes 25: The Zeeman Effect in
Hydrogen and Alkali Atoms, pdf
format.
- Notes 26: Hyperfine Structure in
Atoms, pdf format.
- Notes 27: The Variational
Method, pdf
format.
- Notes 28: Identical
Particles, pdf
format.
- Notes 29: Helium,
pdf
format.
- Notes 30: The Thomas-Fermi
Model, in pdf format.
- Notes 31: The Hartree-Fock
Method in Atoms, in pdf
format.
- Notes 32: Elements of Atomic
Structure in Multi-Electron Atoms, in pdf format.
- Notes 33: Time-Dependent
Perturbation Theory, in pdf
format.
- Notes 34: The Photoelectric
Effect, in pdf
format.
- Notes 35: Introduction to
Scattering Theory and Scattering from Central Force Potentials,
in pdf format.
- Notes 36: Green's Functions in
Quantum Mechanics, in pdf
format.
- Notes 37: The Lippmann-Schwinger
Equation, in pdf
format.
- Notes 38: Adiabatic Invariance,
the Geometric Phase, and the Born-Oppenheimer Approximation, in
pdf format.
- Notes 39: The Classical
Electromagnetic Field Hamiltonian, in pdf format.
- Notes 40: The Quantized
Electromagnetic Field, in pdf
format.
- Notes 41: Emission and
Absorption of Radiation, in pdf
format.
- Notes 42: Scattering of
Radiation, in pdf
format.
- Notes 43: Natural Line Width and the Lamb Shift, in pdf format.
- Notes 44: The Klein-Gordon
Equation, in pdf format.
- Notes 45: Introduction to the
Dirac Equation, in pdf
format.
- Notes 46: Lorentz
Transformations in Special Relativity, in pdf format.
- Notes 47: Covariance of the
Dirac Equation, in pdf format.
- Notes 48: The Foldy-Wouthuysen
Transformation, in pdf format.
- Notes 49: Solutions of the
Dirac Equation, in pdf format.
- Notes 50: Hole Theory and
Second Quantization of the Dirac Field, in pdf format.
- Notes 51: Electromagnetic
Interactions With the Dirac Field, in pdf format.
- Appendix A: Gaussian, SI and
Other Systems of Units in Electromagnetic Theory, pdf format.
- Appendix B: Classical
Mechanics, pdf
format.
- Appendix C: Gaussian
Integrals, pdf
format.
- Appendix D: Vector
Calculus, pdf format.
- Appendix E: Tensor
Analysis, pdf format.
Homework Solutions.
Reprints.
- Table of Clebsch-Gordan
Coefficients, etc in pdf
format only.
- I can do that for you! in pdf format only.
Links to web sites for other
courses I have taught.
Physics 209, Fall 2002.
Physics 250, Fall 2015.