Physics 221AB
Quantum Mechanics
Fall 2020 and Spring 2021
University of California, Berkeley
- Instructor: Robert Littlejohn
- Office: 449 Birge
- Office Hours: Fridays 11am-12
- Email: physics221@wigner.berkeley.edu
GSI: Newton Cheng
GSI's email address: newtoncheng@berkeley.edu
Office Hours: Thursdays, 10-11
-
- Lecture: Internet/Online
- Time: TuTh 6:30-8pm
- Discussion Section 101: Wed 4-5, Online
- Discussion Section 102: Tue 11-12, Online
- Recommended text: Eugene D. Commins, Quantum Mechanics: An Experimentalist's Approach.
-
- Final Exam: Take Home; Available 5pm Monday,
May 10; due 5pm Wednesday, May 12. 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 January 17, 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
Heather Makiharju in the physics department. I will then look at your
transcript and make a recommendation. Admission to Physics 221 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 take home.
See above for details and the link.
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 will have to be sent electronically
to the GSI. You will have to have some means (a scanner, a phone with
a camera, an ipad, etc) to convert your homework to a pdf file that
you can send to the GSI. The homework should be sent to the GSI's
email account, which is newtoncheng@berkeley.edu
with the subject line, "Physics 221B Homework".
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.
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 27, 2020: Notes 1, Secs. 1-18, Video.
- Tuesday, September 1, 2020: Notes 1, Secs. 19-28; Notes 2, Secs. 1-2.
Video.
- Thursday, September 3, 2020: Notes 2, Secs. 3-9; Notes 3, Secs. 1-11.
Video.
- Tuesday, September 8, 2020: Notes 3, Secs. 12-19; Notes 4, Secs. 1-6.
Video.
- Thursday, September 10, 2020: Notes 4, Secs. 7-18; Notes 5, Secs. 1-16.
Video.
- Tuesday, September 15, 2020: Notes 5, Secs. 17-18; Notes 6, entire;
Notes 7, Secs. 1-3.
Video.
- Thursday, September 17, 2020: Notes 7, Secs. 4-11.
Video.
- Tuesday, September 22, 2020: Notes 7, Secs. 12-13; Notes 8,
Secs. 1-9.
Video.
- Thursday, September 24, 2020: Notes 8, Sec. 10; Notes 9,
Secs. 1-9.
Video.
- Tuesday, September 29, 2020:
Video.
- Thursday, October 1, 2020:
Video.
- Tuesday, October 6, 2020:
Video.
- Thursday, October 8, 2020:
Video.
- Tuesday, October 13, 2020:
Video.
- Thursday, October 15, 2020:
Video.
- Tuesday, October 20, 2020:
Video.
- Thursday, October 22, 2020:
Video.
- Tuesday, October 27, 2020:
Video.
- Thursday, October 29, 2020:
Video.
- Tuesday, November 3, 2020:
Video.
- Thursday, November 5, 2020:
Video.
- Tuesday, November 10, 2020:
Video.
- Thursday, November 12, 2020:
Video.
- Tuesday, November 17, 2020:
Video.
- Thursday, November 19, 2020:
Video.
- Tuesday, December 1, 2020:
Video.
- Thursday, December 3, 2020:
Video.
- Tuesday, January 19, 2021: Notes 28, entire; Notes 29,
Secs. 1-6.
Video.
- Thursday, January 21, 2021: Notes 29, Secs. 7-8; Notes
30, Secs. 1-5.
Video.
- Tuesday, January 26, 2021: Notes 30, Secs. 6-10.
Video.
- Thursday, January 28, 2021: Note 30, Secs. 11-12;
Notes 32, Secs. 1-5.
Video.
- Tuesday, February 2, 2021: Notes 32, Secs. 6-11.
Video.
- Thursday, February 4, 2021: Note 32, Secs. 12-14 and 16.
Video.
- Tuesday, February 9, 2021: Notes 33, Secs. 1-10.
Video.
- Thursday, February 11, 2021: Note 34, Secs. 1-12.
Video.
- Tuesday, February 16, 2021: Notes 34, Secs. 13-21.
Video.
- Thursday, February 18, 2021: Note 36, Secs. 1-7.
Video.
- Tuesday, February 23, 2021: Notes 36, Secs. 8-13.
Video.
- Thursday, February 25, 2021: Notes 36, Sec. 14,
Notes 37, Secs. 1-9.
Video.
- Tuesday, March 2, 2021: Notes 37, Secs. 10-16.
Video.
- Thursday, March 4, 2021: Notes 37, Secs. 10-18;
Notes 38, Secs. 1-7.
Video.
- Tuesday, March 9, 2021: Notes 38, Secs. 8 and 10;
Notes 40, Secs. 1-7.
Video.
- Thursday, March 11, 2021: Notes 40, Secs. 8-17.
Video.
- Tuesday, March 16, 2021: Notes 40, Secs. 18-20;
Notes 41, Secs. 1-8.
Video.
- Thursday, March 18, 2021: Notes 41, Secs. 9-15 and
17-18.
Video.
- Tuesday, March 30, 2021: Notes 41, Secs. 19-20,
Notes 42, Secs. 1-6.
Video.
- Thursday, April 1, 2021: Notes 42, Secs. 7-12.
Video.
- Tuesday, April 6, 2021: Notes 43, Secs. 1-7.
Video.
- Thursday, April 8, 2021: Notes 43, Secs. 8-14.
Video.
- Tuesday, April 13, 2021: Notes 44, Secs. 1 and 12;
Notes 45, entire; Notes 46, Secs. 1-4.
Video.
- Thursday, April 15, 2021: Notes 46, Secs. 5-9;
Notes 47, Secs. 1-3.
Video.
- Tuesday, April 20, 2021: Notes 47, Secs. 4-11;
Notes 48, Secs. 1-3.
Video.
- Thursday, April 22, 2021: Notes 48, Secs. 4-11.
Video.
- Tuesday, April 27, 2021: Notes 48, Secs. 12-17;
Notes 49, Secs. 1-5.
Video.
- Thursday, April 29, 2021: Nores 49, Secs. 6-10;
lecture includes a very brief overview of Notes 50-51.
Video.
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. Homework must be submitted electronically, and
you will have to have a means of scanning or converting your homework
into electronic form (a pdf file). Send your homework to
newtoncheng@berkeley.edu
- Homework 1, due Friday, September 4 at 5pm, in pdf format.
- Homework 2, due Friday, September 11 at 5pm, in pdf format.
- Homework 3, due Friday, September 18 at 5pm, in pdf format.
- Homework 4, due Friday, September 25 at 5pm, in pdf format.
- Homework 5, due Friday, October 2 at 5pm, in pdf format.
- Homework 6, due Friday, October 9 at 5pm, in pdf format.
- Homework 7, due Friday, October 16 at 5pm, in pdf format.
- Homework 8, due Friday, October 23 at 5pm, in pdf format.
- Homework 9, due Friday, October 30 at 5pm, in pdf format.
- Homework 10, due Friday, November 6 at 5pm, in pdf format.
- Homework 11, due Friday, November 13 at 5pm, in pdf format.
- Homework 12, due Friday, November 20 at 5pm, in pdf format.
- Homework 13, due Monday, November 30 at 5pm, in pdf format.
- Homework 14, due Friday, December 11 at 5pm, in pdf format.
- Homework 15, due Friday, January 29 at 5pm, in pdf format.
- Homework 16, due Friday, February 5 at 5pm, in pdf format.
- Homework 17, due Friday, February 12 at 5pm, in pdf format.
- Homework 18, due Friday, February 19 at 5pm, in pdf format.
- Homework 19, due Friday, February 26 at 5pm, in pdf format.
- Homework 20, due Friday, March 5 at 5pm, in pdf format.
- Homework 21, due Friday, March 12 at 5pm, in pdf format.
- Homework 22, due Friday, March 19 at 5pm, in pdf format.
- Homework 23, due Friday, April 2 at 5pm, in pdf format.
- Homework 24, due Friday, April 9 at 5pm, in pdf format.
- Homework 25, due Friday, April 16 at 5pm, in pdf format.
- Homework 26, due Friday, April 23 at 5pm, in pdf format.
- Homework 27, due Friday, April 30 at 5pm, in pdf format.
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.