Physics 221B
Quantum Mechanics
Spring 2018
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: Arvin Shahbazi-Moghaddam, Office Hours Thu 9:30-10:30, Panic Room
-
- Lecture: 222 Wheeler
- Time: TuTh 6:30-8pm
- Discussion Section 1: Wed 6-7, B56 Hildebrand
- Discussion Section 2: Tue 8-9, 187 Dwinelle
- Recommended text: Eugene D. Commins, Quantum Mechanics: An Experimentalist's Approach.
-
- Final Exam: Oral, Sunday, May 6 to Tuesday, May 15, 2018; 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 12, 2018, 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.
During the first week only the Wednesday discussion section will
be held.
Prerequisites for
this course include graduate standing and 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 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 6-15.
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. 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.
- Thursday, August 24, 2017: Notes 1, Secs. 1-20.
- Tuesday, August 29, 2017: Notes 1, Secs. 21-26; Notes 2, Secs.
1-3.
- Thursday, August 31, 2017: Notes 2, Secs. 4-9; Notes 3, Secs.
1-11.
- Tuesday, September 5, 2017: Notes 3, Secs. 12-19; Notes 4,
Secs. 1-5.
- Thursday, September 7, 2017: Notes 4, Secs. 6-18; Notes 5,
Secs. 1-11.
- Tuesday, September 12, 2017: Notes 5, Secs. 12-18; Notes 7,
Sec. 13; Notes 8, Secs. 1-6.
- Thursday, September 14, 2017: Notes 6 entire, Notes 8, Secs
7-10.
- Tuesday, September 19, 2017: Notes 9, Secs. 1-9; Notes 10,
Secs. 1-2.
- Thursday, September 21, 2017: Notes 10, Secs 3-6.
- Tuesday, September 26, 2017: Notes 10, Sec. 7; Notes 11, Secs.
1-10 and 12.
- Thursday, September 28, 2017: Notes 11, Sec. 13; Notes 12, Secs.
1-9, 11, 13-14.
- Tuesday, October 3, 2017: Notes 13, Secs. 1-5.
- Thursday, October 5, 2017: Notes 13, Secs. 6-8, Notes 14,
Secs. 1-12.
- Tuesday, October 10, 2017: Notes 14, Secs. 13-14; Notes 15,
Secs. 1-7.
- Thursday, October 12, 2017: Notes 15, Secs. 8-11, Notes 16,
Secs. 1-9.
- Tuesday, October 17, 2017: Notes 16, Secs. 10-11, Notes 17, Secs.
1-8.
- Thursday, October 19, 2017: Notes 17, Secs. 9-10; Notes 18, Secs.
1-12.
- Tuesday, October 24, 2017: Notes 18, Secs. 13-14; Notes 19, Secs.
1-9, 11.
- Thursday, October 26, 2017: Notes 19, Secs. 12-16 and 19; Notes
20, Secs. 1-4.
- Tuesday, October 31, 2017: Notes 20, Secs. 5-11; Notes 21, Secs.
1-10.
- Thursday, November 2, 2017: Notes 21, Secs. 11-19, Notes 22,
Secs. 1-5.
- Tuesday, November 7, 2017: Notes 22, Secs. 6-7; Notes 23, Secs.
1-13.
- Thursday, November 9, 2017: Notes 23, Secs. 14-16; Notes 24,
Secs. 1-9.
- Tuesday, November 14, 2017: Notes 24, Secs. 10-18; Notes 25,
Secs. 1-5.
- Thursday, November 16, 2017: Notes 25, Secs. 6-8; Notes 26,
Secs. 1-5.
- Tuesday, November 28, 2017: Notes 26, Secs. 6-7; Notes 27,
Secs. 1-6.
- Thursday, November 30, 2017: Notes 27, Sec 7; Notes 28 entire.
- Tuesday, January 16, 2018: Notes 29, Secs. 1-10.
- Thursday, January 18, 2018: Notes 29, Secs. 11-12.
- Tuesday, January 23, 2018: Notes 33, Secs. 1-11.
- Thursday, January 25, 2018: Notes 33, Secs. 12-19.
- Tuesday, January 30, 2018: Notes 35, Secs. 1-9.
- Thursday, February 1, 2018: Notes 35, Sec. 10--14; Notes 36,
Secs. 1-4.
- Tuesday, February 6, 2018: Notes 36, Secs. 5-16.
- Thursday, February 8, 2018: Notes 36, Secs. 17-18; Notes
37, Secs. 1-8.
- Tuesday, February 13, 2018: Notes 37, Sec. 10; Notes 39,
Secs. 1-8.
- Thursday, February 15, 2018: Notes 39, Secs. 9-17.
- Tuesday, February 20, 2018: Notes 39, Secs. 18-20; Notes 40,
Secs. 1-7.
- Thursday, February 22, 2018: Notes 40, Secs. 8-15, 17-18.
- Tuesday, February 27, 2018: Notes 40, Secs. 19-21; Notes
41, Secs. 1-3, 5-6.
- Thursday, March 1, 2018: Notes 41, Secs. 4 and 7-11.
- Tuesday, March 6, 2018: Notes 41, Sec. 12; Notes 42, Secs.
1-9.
- Thursday, March 8, 2018: Notes 42, Secs. 10-13; Notes 43, Secs.
1-3.
- Tuesday, March 13, 2018: Notes 43, Secs. 4-7; Notes 44, Secs.
1-8.
- Thursday, March 15, 2018: Notes 44, Sec. 9; Notes 45, Secs.
1-9.
- Tuesday, March 20, 2018: Notes 45, Secs. 10-11; Notes 46,
Secs. 1-7.
- Thursday, March 22, 2018: Notes 46, Secs. 8-16.
- Tuesday, April 3, 2018: Notes 46, Sec. 17; Notes 47, Secs.
1-9.
- Thursday, April 5, 2018: Notes 47, Secs. 10-11; Notes 48,
Secs. 1-6.
- Tuesday, April 10, 2018: Notes 48, Secs. 7-14.
- Thursday, April 12, 2018: Notes 48, Secs. 15-18; Notes 49,
Secs. 1-4.
- Tuesday, April 17, 2018: Notes 49, Secs. 5-10.
- Thursday, April 19, 2018: Notes 49, Secs. 11-15.
- Tuesday, April 24, 2018: Extra lecture on long time behavior and
natural line width.
- Thursday, April 26, 2018: More on natural line width, resonance
fluorescence.
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 221B 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 1 at 5pm, in pdf format.
- Homework 2, due Friday, September 8 at 5pm, in pdf format.
- Homework 3, due Friday, September 15 at 5pm, in pdf format.
- Homework 4, due Friday, September 22 at 6pm, in pdf format.
- Homework 5, due Friday, September 29 at 6pm, in pdf format.
- Homework 6, due Friday, October 6 at 6pm, in pdf format.
- Homework 7, due Friday, October 13 at 6pm, in pdf format.
- Homework 8, due Friday, October 20 at 6pm, in pdf format.
- Homework 9, due Friday, October 27 at 6pm, in pdf format.
- Homework 10, due Friday, November 3 at 6pm, in pdf format.
- Homework 11, due Friday, November 10 at 6pm, in pdf format.
- Homework 12, due Friday, November 17 at 6pm, in pdf format.
- Homework 13, due Monday, November 27 at 6pm, in pdf format.
- Homework 14, due Friday, December 8 at 6pm, in pdf format.
- Homework 15, due Friday, January 19 at 6pm, in pdf format.
- Homework 16, due Friday, January 26 at 6pm, in pdf format.
- Homework 17, due Friday, February 2 at 6pm, in pdf format.
- Homework 18, due Friday, February 9 at 6pm, in pdf format.
- Homework 19, due Friday, February 16 at 6pm, in pdf format.
- Homework 20, due Friday, February 23 at 6pm, in pdf format.
- Homework 21, due Friday, March 2 at 6pm, in pdf format.
- Homework 22, due Friday, March 9 at 6pm, in pdf format.
- Homework 23, due Friday, March 16 at 6pm, in pdf format.
- Homework 24, due Friday, March 23 at 6pm, in pdf format.
- Homework 25, due Friday, April 6 at 6pm, in pdf format.
- Homework 26, due Friday, April 13 at 6pm, in pdf format.
- Unhomework 27, nothing due, in pdf format.
- Homework 28, due Friday, April 27 at 6pm, 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 Ordinary
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: The Klein-Gordon
Equation, in pdf format.
- Notes 44: Introduction to the
Dirac Equation, in pdf
format.
- Notes 45: Lorentz
Transformations in Special Relativity, in pdf format.
- Notes 46: Covariance of the
Dirac Equation, in pdf format.
- Notes 47: Solutions of the
Dirac Equation, in pdf format.
- Notes 48: Hole Theory and
Second Quantization of the Dirac Field, in pdf format.
- Notes 49: 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 6 through Monday,
May 14. 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, except the last week of
lecture (April 24 and 26) will not be covered.
Not all material in the notes will be on the exam. Here is a list of
the material from the notes that will and will not be covered in the
exam: All material from Notes 28 (on identical particles) through
Notes 49, except you may skip Notes 30, 31, 32, 34 and 38, which were
not covered in lecture; and you may skip Sec. 37.9 (on the T-matrix)
and Sec. 40.16 (on the orbital angular momentum of the photon) and
Sec. 40.21 (on vector multipole fields), which also were not covered.
These section numbers refer to the current set of notes on the
website; in some cases the numbering has changed slightly since the
beginning of the semester.
You may also bring along 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 6:
- 9:00am: Taken
- 10:20am: Taken
- 12:10pm: Taken
- 1:30pm: Taken
- 2:50pm: Taken
- 4:10pm: Taken
Monday, May 7:
- 8:30am: Taken
- 9:50am: Taken
- 11:10am: Taken
- 12:30pm: Taken
- 1:50pm: Taken
Tuesday, May 8:
- 8:30am: Taken
- 9:50am: Taken
- 11:10am: Taken
- 1:00pm: Taken
- 2:20pm: Taken
- 3:40pm: Taken
Wednesday, May 9:
- 9:00am: Taken
- 10:20am: Taken
- 2:00pm: Taken
- 3:20pm: Taken
- 4:40pm: Taken
Thursday, May 10:
- 9:00am: Free
- 10:20am: Taken
- 12:10pm: Taken
- 1:30pm: Taken
- 2:50pm: Taken
- 4:10pm: Taken
Friday, May 11:
- 9:00am: Taken
- 10:20am: Taken
- 12:10pm: Taken
- 1:30pm: Taken
- 2:50pm: Taken
- 4:10pm: Taken
Saturday, May 12:
- 9:00am: Taken
- 10:20am: Taken
- 12:10pm: Taken
- 1:30pm: Taken
- 2:50pm: Taken
- 4:10pm: Taken
Monday, May 14:
- 9:00am: Taken
- 10:20am: Taken
- 11:40am: 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.