Physics 221B
Quantum Mechanics
Spring 2016
University of California, Berkeley
- Instructor: Robert Littlejohn
- Office: 449 Birge
- Office Hours: Friday 1-2
- Telephone: 642-1229
- Email: physics221@wigner.berkeley.edu
TA: Eugene Kur, Office Hours Thursdays 3-4, 429 Birge
-
- Lecture: 213 Wheeler
- Time: TuTh 6-7:30pm
- Discussion Section 1: Wed 2-3, 102 Lattimer
- Discussion Section 2: Tu 8-9am, 30 Wheeler
- Recommended text: Eugene D. Commins, Quantum Mechanics: An Experimentalist's Approach.
-
- Final Exam: Oral, Sunday, May 8 to Tuesday, May 17; 449 Birge; See instructions below for signup.
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 15, 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. I will
probably cancel one official discussion section and reschedule the other for
Thursday afternoon.
Prerequisites for
this course include graduate standing, Physics 221A, and a background
in special relativity such as taught in Physics 209. 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. Later I will ask students to sign up for time slots for
the oral during the week of May 8 to 17.
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 in 251 LeConte (the reading room).
I'm going to try to reschedule the discussion section on Thursday, so
it will be one day before the homework is due (on Friday).
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.
- Tuesday, January 19, 2016: For Dirac notation, read Notes 1,
Secs. 2-6 or more as needed; for the density operator, read Notes 3,
Secs. 1-8 or more; for translation operators and the momentum as the
generator of translations, read Notes 4, Secs. 3-6 or more.
- Thursday, January 21, 2016: For rotations in three-dimensional
space, read Notes 11, Secs. 1-10 and 12; for the rotation of wave
functions in 3d and orbital angular momentum, read Notes 15,
Secs. 1-3.
- Tuesday, January 26, 2016: For rotations of spin 1/2 system,
read Notes 12, Secs. 1-9 and 13-14. If you need to review the
derivation of angular momentum algebra, read Notes 13, Secs. 1-4; in
any case, read Secs. 5-7.
- Thursday, January 28, 2016: For the generalized adjoint formula,
read Notes 13, Sec. 9; for spins in magnetic fields, read Notes 14,
Secs. 3-5 and 10-11; for some useful identities involving spherical
harmonics, read Notes 15, Secs. 7 and 8; for review of central force
motion, read Notes 16, Secs. 1-4. Please also see the link to the
table of Clebsch-Gordan coefficients, spherical harmonics and
d-functions (reduced rotation matrices).
- Tuesday, February 2, 2016: For other topics in central force
motion, please read Note 15, Secs 5-7 and 9; for the hydrogen atom,
see the notes; for
including spin and the Pauli equation, see the notes; for coupling of
angular momentum and Clebsch-Gordan coefficients, see Notes 17,
Secs 1-9 if you need review.
- Thursday, February 4, 2016: For the 3 Ylm formula, see Notes
17, Secs 10 and 11; for the transformation properties of operators
under rotations, see Notes 18, Secs 1-9.
- Tuesday, February 9, 2016: Notes 18, Secs 11-16; and Secs 17-18
if you want to see a real proof of the Wigner-Eckart
theorem; Notes 23, Secs. 1-3.
- Thursday, February 11, 2016: Notes 23, Secs 4-15. If you need
review on perturbation theory, see Notes 21.
- Tuesday, February 16, 2016: The first part of the lecture
concerned parity and selection rules. See Notes 19 Sec. 11, as well
as other sections of those notes if you need review about parity.
Also please read Notes 25, Secs 1-4.
- Thursday, February 18, 2016: Notes 25, Secs 5-6; Notes 27,
Secs. 1-5.
- Tuesday, February 23, 2016: Notes 27, Secs. 6-8; Notes 28, Secs 1-5.
- Thursday, February 25, 2016: Notes 28, Secs 6-10 and 12.
- Tuesday, March 1, 2016: Notes 28, Sec 11; Notes 32, Secs 1-6.
- Thursday, March 3, 2016: Notes 32, Secs 7-13.
- Tuesday, March 8, 2016: Rest of Notes 32, Notes 38, Secs. 1-4.
- Thursday, March 10, 2016: Notes 38, Secs. 5-10.
- Tuesday, March 15, 2016: Notes 38, Secs. 11-18.
- Thursday, March 17, 2016: Notes 38, Secs. 18-20; Notes 40, Secs.
1-6.
- Tuesday, March 29, 2016: Notes 40, Secs. 6-10.
- Thursday, March 31, 2016: Notes 40, Secss 11-12, and bottom of
p. 20 to end; Notes 41, Secs. 1-4.
- Tuesday, April 5, 2016: Notes 41, Secs. 5-8.
- Thursday, April 7, 2016: Notes 41, Secs. 9-12.
- Tuesday, April 12, 2016: Notes 43; Notes 44, Secs. 1-7.
- Thursday, April 14, 2016: Notes 44, Secs. 8-9; Notes 45, Secs.
1-6.
- Tuesday, April 19, 2016: Notes 45, Secs. 7-12; Notes 46, Secs.
1-5.
- Thursday, April 21, 2016: Notes 46, Secs. 6-12.
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 221B homework box in 251 LeConte (the reading room).
- Homework 1, due Friday, January 29 at 5pm, in pdf format.
- Homework 2, due Friday, February 5 at 5pm, in pdf format.
- Homework 3, due Friday, February 12 at 5pm, in pdf format.
- Homework 4, due Friday, February 19 at 5pm, in pdf format.
- Homework 5, due Friday, February 26 at 5pm, in pdf format.
- Homework 6, due Friday, March 4 at 5pm, in pdf format.
- Homework 7, due Friday, March 18 at 5pm, in pdf format.
- Homework 8, due Friday, April 1 at 5pm, in pdf format.
- Homework 9, due Friday, April 8 at 5pm, in pdf format.
- Homework 10, due Friday, April 15 at 5pm, in pdf format.
- Homework 11, due Friday, April 22 at 5pm, in pdf format.
- Homework 12, due Friday, April 29 at 5pm, in pdf format.
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: Coupling of Angular
Momenta, pdf format.
- Notes 18: Irreducible Tensor
Operators and the Wigner-Eckart Theorem, pdf format.
- Notes 19: Parity, pdf format.
- Notes 20: Time Reversal,
pdf format.
- Notes 21: Bound-State Perturbation
Theory, pdf format.
- Notes 22: The Stark Effect in
Hydrogen and Alkali Atoms, in pdf
format.
- Notes 23: Fine Structure in
Hydrogen and Alkali Atoms, pdf format.
- Notes 24: The Zeeman Effect in
Hydrogen and Alkali Atoms, pdf
format.
- Notes 25: Hyperfine Structure in
Atoms, pdf format.
- Notes 26: The Variational
Method, pdf
format.
- Notes 27: Identical
Particles, pdf
format.
- Notes 28: Helium and Helium-like
Atoms, pdf format.
- Notes 29: The Thomas-Fermi
Model, pdf format.
- Notes 30: The Hartree-Fock
Method in Atoms, pdf
format.
- Notes 31: Elements of Atomic
Structure in Multi-Electron Atoms, in pdf format.
- Notes 32: Time-Dependent
Perturbation Theory, in pdf
format.
- Notes 33: The Photoelectric
Effect, in pdf
format.
- Notes 34: Introduction to
Scattering Theory and Scattering from Central Force Potentials,
in pdf format.
- Notes 35: Green's Functions in
Quantum Mechanics, in pdf
format.
- Notes 36: The Lippmann-Schwinger
Equation, in pdf
format.
- Notes 37: Adiabatic Invariance,
the Geometric Phase, and the Born-Oppenheimer Approximation, in
pdf format.
- Notes 38: The Classical
Electromagnetic Field Hamiltonian, in pdf format.
- Notes 39: Lagrangian and
Hamiltonian Formulation of the Classical Electromagnetic Field,
in pdf format.
- Notes 40: The Quantized
Electromagnetic Field, in pdf
format.
- Notes 41: Interaction of
Radiation with Matter, 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.
- 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 8 through Tuesday May 17. 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 week (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. Things that were not
covered in these areas will not be on the exam (for example, sets of
notes that were never listed in a reading assignment).
You may also bring along a friend, 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 8:
- 7:45am: Free
- 9:00am: Taken
- 10:15am: Taken
- 11:30am: Taken
- 12:45am: Taken
- 2:00pm: Taken
- 3:15pm: Taken
- 4:30pm: Taken
Monday, May 9:
- 8:30am: Taken
- 9:45am: Taken
- 11:00am: Taken
- 12:15pm: Taken
- 1:30pm: Taken
Tuesday, May 10:
- 8:30am: Taken
- 9:45am: Taken
- 11:00am: Taken
- 12:15pm: Taken
- 1:30pm: Taken
Wednesday, May 11:
- 7:00am: Free
- 8:15am: Free
- 9:30am: Taken
- 10:45am: Taken
- 2:30pm: Taken
- 3:45pm: Taken
Thursday, May 12:
- 7:00am: Free
- 8:15am: Taken
- 9:30am: Taken
- 10:45am: Taken
- 12:00noon: Taken
- 1:15pm: Taken
- 2:30pm: Taken
- 3:45pm: Taken
Friday, May 13:
- 7:00am: Free
- 8:15am: Taken
- 9:30am: Taken
- 10:45am: Taken
- 12:00noon: Taken
- 1:15pm: Taken
- 2:30pm: Taken
- 3:45pm: Taken
Saturday, May 14:
- 7:00am: Free
- 8:15am: Taken
- 9:30am: Taken
- 10:45am: Taken
- 12:00noon: Taken
- 1:15pm: Taken
- 2:30pm: Taken
- 3:45pm: Taken
Monday, May 16:
- 8:30am: Taken
- 9:45am: Taken
- 11:00am: Taken
- 12:15pm: Taken
- 1:30pm: Taken
Tuesday, May 17:
- 8:30am: Taken
- 9:45am: Taken
- 11:00am: Taken
- 12:15pm: Taken
- 1:30pm: Taken
Homework Solutions.
Reprints.
- Table of Clebsch-Gordan
Coefficients, etc in pdf
format only.
Links to web sites for other courses I have taught.
Physics 209, Fall 2002.
Physics 250, Fall 2015.