Physics 221AB
Quantum Mechanics
Fall 2018 and Spring 2019
University of California, Berkeley
- Instructor: Robert Littlejohn
- Office: 449 Birge
- Office Hours: Fridays 12:30-1:30
- Telephone: 642-1229
- Email: physics221@wigner.berkeley.edu
TA: Chris Akers
Office Hours: Thursdays 10-11am, Panic Room (4th Floor Birge)
-
- Lecture: 251 LeConte
- Time: TuTh 6:30-8pm
- Discussion Section 101: Wed 3-4, 3109 Etcheverry
- Discussion Section 102: Tue 4-5, 109 Dwinelle (but will probably change)
- Recommended text: Eugene D. Commins, Quantum Mechanics: An Experimentalist's Approach.
-
- Final Exam: Oral, Sunday, May 12 to Tuesday, May 21, 2019; 449 Birge.
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 Friday, January 18, 2019, 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. I am planning an oral final exam
this semeter. To obtain full credit for the homework it will be
necessary to show some knowledge of the homework problems on the final
exam. Later I will ask students to sign up for time slots for the
oral during the period May 12 to 21, 2019.
Weekly homework
assignments will be made available on this web site (usually)
by Saturday of each week, and will be due at 6pm 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 23, 2018: Notes 1, Secs. 1-20.
- Tuesday, August 28, 2018: Notes 1, Secs. 21-26; Notes 2, Secs.
1-3.
- Thursday, August 30, 2018: Notes 2, Secs. 4-9; Notes 3, Secs.
1-12.
- Tuesday, September 4, 2018: Notes 3, Secs. 13-19; Notes 4, Secs.
1-7.
- Thursday, September 6, 2018: Notes 4, Secs. 8-18, Notes 5, Secs.
1-13.
- Tuesday, September 11, 2018: Notes 5, Secs. 14--18; Notes 7, Secs.
1-5.
- Thursday, September 13, 2018: Notes 7, Secs. 6-11.
- Tuesday, September 18, 2018: Notes 7, Secs. 12-13; Notes 6, entire;
Notes 8, Secs. 1-8.
- Thursday, September 20, 2018: Notes 8, Secs. 9-10; Notes 9, Secs. 1-4.
- Tuesday, September 25, 2018: Notes 9, Secs. 5-9, Notes 10, Secs. 1-4.
- Thursday, September 27, 2018: Notes 10, Secs. 5-7.
- Tuesday, October 2, 2018: Notes 11, Secs. 1-13.
- Thursday, October 4, 2018: Notes 12, Secs. 1-11 and 13-14, Notes
13, Secs. 1-2.
- Tuesday, October 9, 2018: Notes 13, Secs. 3-5 and 8
- Thursday, October 11, 2018: Notes 13, Secs. 6-7, Notes 14,
Secs. 1-5 and 10-14.
- Tuesday, October 16, 2018: Notes 15 entire; Notes 16, Secs. 1-2.
- Thursday, October 18, 2018: Notes 16, Secs. 3-11.
- Tuesday, October 23, 2018: Notes 17 entire, Notes 18, Secs. 1-3.
- Thursday, October 25, 2018: Notes 18, Secs. 4-14; Notes 19, Secs.
1-6.
- Tuesday, October 30, 2018: Notes 19, Secs. 7-16 and 19.
- Thursday, November 1, 2018: Notes 20, entire; Notes 21,
Secs. 1-5.
- Tuesday, November 6, 2018: Notes 21, Secs. 6-19; Notes 22, Secs.
1-2.
- Thursday, November 8, 2018: Notes 22, Secs. 3-7; Notes 23, Secs.
1-14.
- Tuesday, November 13, 2018: Notes 23, Secs. 15-16; Notes 24, Secs.
1-10.
- Thursday, November 15, 2018: Smoked out.
- Tuesday, November 20, 2018: Smoked out again.
- Tuesday, November 27, 2018: Notes 24, Secs. 11-18; Notes 25,
Secs. 1-6.
- Thursday, November 29, 2018: Notes 25, Secs. 7-8, Notes 26,
Secs. 1-4.
- Tuesday, December 4, 2018: Notes 26, Secs. 5-7.
- Tuesday, January 22, 2019: Notes 27, entire; Notes 28, entire.
- Thursday, January 24, 2019: Notes 29, Secs. 1-8.
- Tuesday, January 29, 2019: Notes 29, Secs. 9-12.
- Thursday, January 31, 2019: Notes 31, Secs. 1-10.
- Tuesday, February 5, 2019: Notes 31, Secs. 11-14.
- Thursday, February 7, 2019: Notes 31, Sec. 16; Notes 32,
Secs. 1-8
- Tuesday, February 12, 2019: Notes 32, Secs. 9-10, Notes 33,
Secs. 1-7.
- Thursday, February 14, 2019: Notes 33, Secs. 8-19.
- Tuesday, February 19, 2019: Notes 35, Secs. 1-8.
- Thursday, February 21, 2019: Notes 35, Secs. 9-13.
- Tuesday, February 26, 2019: Notes 35, Sec. 14; Notes 36,
Secs. 1-7.
- Thursday, February 28, 2019: Notes 36, Secs. 8--18; Notes
37, Secs. 1-2.
- Tuesday, March 5, 2019: Notes 37, Secs. 3-8 and 10; Notes 39,
Sec. 1.
- Thursday, March 7, 2019: Notes 39, Secs. 2-15.
- Tuesday, March 12, 2019: Notes 39, Secs 16--20; Notes 40,
Secs. 1-6.
- Thursday, March 14, 2019: Notes 40, Secs. 7-12.
- Tuesday, March 19, 2019: Notes 40, Secs. 13-15 and 17-21
(omit) Sec. 16.
- Thursday, March 21, 2019: Notes 41, Secs. 1-7.
- Tuesday, April 2, 2019: Notes 41, Secs. 8-12; Notes 42,
Secs. 1-4.
- Thursday, April 4, 2019: Notes 42, Secs. 5-12.
- Tuesday, April 9, 2019: Notes 42, Secs. 13-14; Notes 43,
Secs. 1-6.
- Thursday, April 11, 2019: Notes 43, Secs. 7-12.
- Tuesday, April 16, 2019: Hand-written notes;
Notes 44, Secs. 1-6.
- Thursday, April 18, 2019: Notes 44, Sec. 7; Notes 45 entire.
- Tuesday, April 23, 2019: Notes 46, entire; Notes 47, Secs.
1,2 and 4.
- Thursday, April 25, 2019: Notes 47, Secs. 3 and 5-11.
Homework
assignments will normally be made available on this web site by
Friday or Saturday of each week, and will be due at 6pm 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, August 31 at 5pm, in pdf format.
- Homework 2, due Friday, September 7 at 5pm, in pdf format.
- Homework 3, due Friday, September 14 at 5pm, in pdf format.
- Homework 4, due Friday, September 21 at 5pm, in pdf format.
- Homework 5, due Friday, September 28 at 5pm, in pdf format.
- Homework 6, due Friday, October 5 at 5pm, in pdf format.
- Homework 7, due Friday, October 12 at 5pm, in pdf format.
- Homework 8, due Friday, October 19 at 5pm, in pdf format.
- Homework 9, due Friday, October 26 at 5pm, in pdf format.
- Homework 10, due Friday, November 2 at 5pm, in pdf format.
- Homework 11, due Friday, November 9 at 5pm, in pdf format.
- Homework 12, due Friday, November 16 at 5pm, in pdf format.
- Homework 13, due Friday, December 7 at 5pm, in pdf format.
- Homework 14, due Friday, February 1 at 5pm, in pdf format.
- Homework 15, due Friday, February 8 at 5pm, in pdf format.
- Homework 16, due Friday, February 15 at 5pm, in pdf format.
- Homework 17, due Friday, February 22 at 5pm, in pdf format.
- Homework 18, due Friday, March 1 at 5pm, in pdf format.
- Homework 19, due Friday, March 8 at 5pm, in pdf format.
- Homework 20, due Friday, March 15 at 5pm, in pdf format.
- Homework 21, due Monday, April 1 at 5pm, in pdf format.
- Homework 22, due Friday, April 5 at 5pm, in pdf format.
- Homework 23, due Friday, April 12 at 5pm, in pdf format.
- Homework 24, due Friday, April 19 at 5pm, in pdf format.
- Homework 25, due Friday, April 26 at 5pm, in pdf format.
- Homework 26, due Friday, May 3 at 5pm, 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.
The Final (Oral)
Exam will be given Sunday, May 12 through Tuesday,
May 21. The exam will last one hour and ten minutes. It will
be held in 449 Birge (my office). Please choose three time slots
during that period (in order of preference), and I will give you the
time slot highest on your list that is still available. Time slots
will be allocated on a first-come-first-served basis.
I will try to break the 70-minute exam period into three or four
sessions, each focusing on a topic covered in the semester. However,
once a line of questioning is started, it can go anywhere within the
material covered during the semester. Oral exams tend to test
physical understanding first and computational details second, so let
that guide you when you study. Fair topics are anything covered in
lecture, reading assignments, or homework.
Material covered by the exam will include Notes 27, 28, 29; all of
Notes 31 except Sec. 15 (on Koopmans' theorem); all of Notes 32, 33,
35, 36; all of Notes 37 except Sec. 9 (on the transition operator);
all of Notes 39; all of Notes 40 except Sec. 16 (on the orbital
angular momentum of the field); all of Notes 41, 42 and 43;
handwritten notes of April 16 on the Lamb shift; all of notes 44, 45,
46, 47 and 48.
You may skip Notes 30, 34, 38.
You may bring a friend to your oral exam, for company and
moral support, but it cannot be someone who is scheduled to take the
oral exam after you. After you have taken your oral exam, you must
not discuss it with anyone in the class before all the exams are
finished.
The grades will be on a scale from 1 to 7, but no grades will be
assigned until all the exams are completed.
Sunday, May 12:
- 9:20am: Taken
- 10:40am: Taken
- 12:30pm: Taken
- 1:50pm: Taken
- 3:10pm: Taken
- 4:30pm: Taken
Monday, May 13:
- 8:40am: Taken
- 10:00am: Taken
- 11:20am: Taken
- 12:40pm: Taken
- 2:00pm: Taken
Tuesday, May 14:
- 8:40am: Taken
- 10:00am: Taken
- 11:50am: Taken
- 1:10pm: Taken
- 2:30pm: Taken
- 3:50pm: Taken
Wednesday, May 15:
- 8:00am: Taken
- 9:20am: Taken
- 10:40am: Taken
- 12:30pm: Taken
- 1:50pm: Taken
- 3:10pm: Taken
Thursday, May 16:
- 8:00am: Taken
- 9:20am: Taken
- 10:40am: Taken
- 12:30pm: Taken
- 1:50pm: Taken
- 3:10pm: Taken
Friday, May 17:
- 8:00am: Taken
- 9:20am: Taken
- 10:40am: Taken
- 12:30pm: Taken
- 1:50pm: Taken
- 3:10pm: Taken
Sunday, May 19:
- 9:20am: Taken
- 10:40am: Taken
- 12:30pm: Taken
- 1:50pm: Taken
- 3:10pm: Taken
- 4:30pm: Taken
Monday, May 20:
- 8:40am: Taken
- 10:00am: Taken
- 11:20am: Taken
- 12:40pm: Taken
- 2:00pm: Taken
Tuesday, May 21:
- 8:40am: Taken
- 10:00am: Taken
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.