Physics 221AB
Quantum Mechanics
Fall 2021 and Spring 2022
University of California, Berkeley
- Instructor: Robert Littlejohn
- Office: 449 Birge
- Office Hours: Fridays 10:30am-11:30am,
397 Physics North
- Email: physics221@wigner.berkeley.edu
-
GSI: Erik Aldape
GSI's email address: e.aldape@berkeley.edu
Office Hours: Fri 9-10, 397 Physics Bldg
-
- Lecture: 166 Social Sciences Bldg
- Time: TuTh 6:30-8pm
- Discussion Section 101: Wed 4-5. 105 Dwinelle
- Discussion Section 102: Tue 10-11, 151 Social
Science Building
- Links to lectures, office hours and discussion
sections may be found here
(UC password required).
- Recommended text: Eugene D. Commins, Quantum Mechanics: An Experimentalist's Approach.
-
- Final Exam: In class, location Physics Bldg 2; Exam
Group 18, Friday, May 13, 11:30-2:30pm.
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 August 22, 2021, 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.
Prerequisites for
221B include 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,
electricity and magnetism and special relativity to do this course.
Graduate students from other departments are advised that some
knowledge of these subjects will be required for Physics 221B.
Physics 221B will require a knowledge of special relativity at the
level of Physics 209.
Undergraduates wishing to take this course must make an application to
Anna Hilke in the physics department. You have my permission to take
221B if you have previously passed 221A with a B or better. Admission
to Physics 221B will also require approval of the head faculty
advisor.
The grade will be
based on homework and a final exam. The final exam will be in class.
See above for time and location.
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. As of February 11, 2022, homeworks should be
submitted as a pdf file at http://gradescope.com/. See the email sent
to all enrolled students on February 10 regarding the code you need to
set up an account with gradescope.
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. You can use your
free late homework for any purpose you wish (illness, travel, etc), 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.
- Homework 1, due Friday, September 3 at 5pm, in pdf format.
- Homework 2, due Friday, September 10 at 5pm, in pdf format.
- Homework 3, due Friday, September 17 at 5pm, in pdf format.
- Homework 4, due Friday, September 24 at 5pm, in pdf format.
- Homework 5, due Friday, October 1 at 5pm, in pdf format.
- Homework 6, due Friday, October 8 at 5pm, in pdf format.
- Homework 7, due Friday, October 15 at 5pm, in pdf format.
- Homework 8, due Friday, October 22 at 5pm, in pdf format.
- Homework 9, due Friday, October 29 at 5pm, in pdf format.
- Homework 10, due Friday, November 5 at 5pm, in pdf format.
- Homework 11, due Friday, November 12 at 5pm, in pdf format.
- Homework 12, due Friday, November 19 at 5pm, in pdf format.
- Homework 13, due Monday, November 29 at 5pm, in pdf format.
- Homework 14, due Thursday, December 9 at 5pm, in pdf format.
- Homework 15, due Friday, January 28 at 5pm, in pdf format.
- Homework 16, due Friday, February 4 at 5pm, in pdf format.
- Homework 17, due Friday, February 11 at 5pm, in pdf format.
- Homework 18, due Friday, February 18 at 5pm, in pdf format.
- Homework 19, due Friday, February 25 at 5pm, in pdf format.
- Homework 20, due Friday, March 4 at 5pm, in pdf format.
- Homework 21, due Friday, March 11 at 5pm, in pdf format.
- Homework 22, due Friday, March 18 at 5pm, in pdf format.
- Homework 23, due Friday, April 1 at 5pm, in pdf format.
- Homework 24, due Friday, April 8 at 5pm, in pdf format.
- Homework 25, due Friday, April 15 at 5pm, in pdf format.
- Homework 26, due Friday, April 22 at 5pm, in pdf format.
- Homework 27, due Friday, May 6 at 5pm, in pdf format.
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.
- Thursday, August 26, 2021: Notes 1, Secs. 1-17. Video.
- Tuesday, August 31, 2021: Notes 1, Secs. 18-28, Notes 2,
Secs. 1-2. Video.
- Thursday, September 2, 2021: Notes 2, Secs. 3-9; Notes 3,
Secs. 1-5. Video.
- Tuesday, September 7, 2021: Notes 3, Secs. 6-19; Notes 4, Secs.
1-7. Video.
- Thursday, September 9, 2021: Notes 4, Secs. 8-18; Notes 5, Secs.
1-16. Video.
- Tuesday, September 14, 2021: Notes 5, Secs. 17-18; Notes 6,
entire; Notes 7, Secs. 1-3. Video.
- Thursday, September 16, 2021: Notes 7, Secs. 4-11.
Video.
- Tuesday, September 21, 2021: Notes 7, Secs. 12-13; Notes 8,
Secs. 1-8. Video.
- Thursday, September 23, 2021: Notes 8, Secs. 9-10; Notes 9,
Secs. 1-4. Video.
- Tuesday, September 28, 2021: Notes 9, Secs. 5-13, 16-17; Notes
10, Secs. 1-2. Video.
- Thursday, September 30, 2021: Notes 10, Secs. 3-6.
Video.
- Tuesday, October 5, 2021: Notes 10, Secs. 7-8; Notes 11,
Secs. 1-8. Video.
- Thursday, October 7, 2021: Notes 11, Secs. 9-14 (you may skip
Sec. 15); Notes 12, Secs. 1-8. Video.
- Tuesday, October 12, 2021: Notes 12, Secs. 9, 11, 13-14 (you may
skip Secs. 10 and 12); Notes 13, Secs. 1-8, 10 (you may skip Sec. 9).
Video.
- Thursday, October 14, 2021: Notes 13, Secs. 11-12; Notes 14,
Secs. 1-7. Video.
- Tuesday, October 19, 2021: Notes 14, Secs. 8-9; Notes 15, entire.
Video.
- Thursday, October 21, 2021: Notes 16, Secs. 1-10.
Video.
- Tuesday, October 26, 2021: Notes 16, Sec. 11, Notes 17, entire.
Video.
- Thursday, October 28, 2021: Notes 18, entire.
Video.
- Tuesday, November 2, 2021: Notes 19, entire; Notes 20,
Secs. 1-2. Video.
- Thursday, November 4, 2021: Notes 20, Secs. 3-9, 12 (you may skip
Secs. 10-11); Notes 21, Secs. 1-4. Video.
- Tuesday, November 9, 2021: Notes 21, Secs. 5-11; Notes 22,
Secs. 1-9. Video.
- Thursday, November 4, 2021: No class.
- Tuesday, November 16, 2021: Notes 22, Secs. 10-19; Notes 23,
Secs. 1-5. Video.
- Thursday, November 18, 2021: Notes 23, Secs. 6-7; Notes 24,
entire. Video.
- Tuesday, November 23, 2021: Notes 25, Secs. 1-14.
Video.
- Thursday, November 25, 2021: Holiday, no class.
- Tuesday, November 30, 2021: Notes 25, Secs. 15-18; Notes 26,
entire; Notes 27, Secs. 1-3. No video available.
- Thursday, December 2, 2021: Notes 27, Secs. 4-8.
Video.
- Tuesday, January 18, 2022: Notes 28, entire; Notes 29,
entire. Video.
- Thursday, January 20, 2022: Notes 30, Secs. 1-7.
Video.
- Tuesday, January 25, 2022: Notes 30, Secs. 8-11. Video.
- Thursday, January 27, 2022: Notes 30, Sec. 12; Notes 32,
Secs. 1-6. Video.
- Tuesday, February 1, 2022: Notes 32, Secs. 7-13. Video.
- Thursday, February 3, 2022: Notes 32, Secs. 14 and 16 (skip 15);
Notes 33, Secs. 1-8.
Video.
- Tuesday, February 8, 2022: Notes 33, Secs. 9-10, Notes 34,
Secs. 1-3. Video.
- Thursday, February 10, 2022: Notes 34, Secs. 4-14.
Video.
- Tuesday, February 15, 2022: Notes 34, Secs. 15-21; Notes 36,
Secs. 1-8. Video.
- Thursday, February 17, 2022: Notes 36, Secs. 9-15.
Video.
- Tuesday, February 22, 2022: Notes 36, Secs. 16-17; Notes 37,
Secs. 1-4. Video.
- Thursday, February 14, 2022: Notes 37, Secs. 5-14.
Video.
- Tuesday, March 1, 2022: Notes 37, Secs. 15-19; Notes 38,
Secs. 1-5. Video.
- Thursday, March 3, 2022: Notes 38, Secs. 6-10; Notes 39, p. 1.
Video.
- Tuesday, March 8, 2022: Notes 39, pp. 2-12.
Video.
- Thursday, March 10, 2022: Notes 40, Secs. 1-9.
Video.
- Tuesday, March 15, 2022: Notes 40, Secs. 10-17.
- Thursday, March 22, 2022: Notes 40, Secs. 18-20;
Notes 41, Secs. 1-8.
- Tuesday, March 29, 2022: Notes 41, Secs. 9-15,
17.
- Thursday, March 31, 2022: Notes 41, Secs. 18-21,
Notes 42, Secs. 1-4.
- Tuesday, April 5, 2022: Notes 42, Secs. 5-10.
- Thursday, April 7, 2022: Notes 42, Secs. 11-12;
Notes 43, Secs. 1-8.
- Tuesday, April 12, 2022: Notes 43, Secs. 9-14;
Notes 44, Secs. 1-2.
- Thursday, April 14, 2022: Notes 44, Secs. 3-9.
- Tuesday, April 19, 2022: Notes 44, Secs. 10-12;
Notes 45, Secs. 1-2.
- Thursday, April 21, 2022: Notes 45, Secs. 3-7,
Notes 46, Secs. 1-7.
Video.
Interesting Movies.
Typed lecture
notes are available for most lectures, not all.
- 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: Transformation
of Operators Under Rotations, pdf format.
- Notes 20: The Wigner-Eckart
Theorem, pdf format.
- Notes 21: Parity, pdf format.
- Notes 22: Time Reversal,
pdf format.
- Notes 23: Bound-State Perturbation
Theory, pdf format.
- Notes 24: The Stark Effect in
Hydrogen and Alkali Atoms, in pdf
format.
- Notes 25: Fine Structure in
Hydrogen and Alkali Atoms, pdf format.
- Notes 26: The Zeeman Effect in
Hydrogen and Alkali Atoms, pdf
format.
- Notes 27: Hyperfine Structure in
Atoms, pdf format.
- Notes 28: The Variational
Method, pdf
format.
- Notes 29: Identical
Particles, pdf
format.
- Notes 30: Helium,
pdf
format.
- Notes 31: The Thomas-Fermi
Model, in pdf format.
- Notes 32: The Hartree-Fock
Method in Atoms, in pdf
format.
- Notes 33: Elements of Atomic
Structure in Multi-Electron Atoms, in pdf format.
- Notes 34: Time-Dependent
Perturbation Theory, in pdf
format.
- Notes 35: The Photoelectric
Effect, in pdf
format.
- Notes 36: Introduction to
Time-Independent Scattering Theory,
in pdf format.
- Notes 37: Green's Functions in
Quantum Mechanics, in pdf
format.
- Notes 38: The Lippmann-Schwinger
Equation, in pdf
format.
- Notes 39: Adiabatic Invariance,
the Geometric Phase, and the Born-Oppenheimer Approximation, in
pdf format.
- Notes 40: The Classical
Electromagnetic Field Hamiltonian, in pdf format.
- Notes 41: The Quantized
Electromagnetic Field, in pdf
format.
- Notes 42: Emission and
Absorption of Radiation, in pdf
format.
- Notes 43: Scattering of
Radiation, in pdf
format.
- Notes 44: Natural Line Width and the Lamb Shift, in pdf format.
- Notes 45: The Klein-Gordon
Equation, in pdf format.
- Notes 46: Introduction to the
Dirac Equation, in pdf
format.
- Notes 47: Lorentz
Transformations in Special Relativity, in pdf format.
- Notes 48: Covariance of the
Dirac Equation, in pdf format.
- Notes 49: The Foldy-Wouthuysen
Transformation, in pdf format.
- Notes 50: Solutions of the
Dirac Equation, in pdf format.
- Notes 51: Hole Theory and
Second Quantization of the Dirac Field, in pdf format.
- Notes 52: 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.