PHYS721/821 - Graduate Quantum Mechanics II

General Information

This is the second semester of the Graduate Quantum Mechanics sequence at ODU. See here for the first semester.


Dr. Sebastian E. Kuhn

Time and Location:

Tuesdays and Thursdays, 5:45 - 7:00 p.m., Room 202 OCNPS
Recitation Sessions by mutual agreement: Fridays 3-4 p.m.

Course Material:

Recommended Books (sorted by match with lecture content)

  1. R. Shankar: "Principles of Quantum Mechanics", 2nd Ed. Springer 1994. I will follow the general approach and much of the material of this book, while leaving some of the more advanced topics to the 2nd semester (PHYS821). If at all possible, buy this book - we will use it most extensively!
  2. G. Arfken: "Mathematical Methods for Physicists" - the best collection of all the math needed by most Physicists
  3. A. Messiah: "Quantum Mechanics" (2-volume edition bound as 1 book), Dover Publication 1999. A comprehensive collection of material, cheap on Amazon etc.
  4. D. Griffiths: "Introduction to Quantum Mechanics", 2nd edition (Pearson 2005) and S. Gasiorowicz: "Quantum Physics" 3rd edition (Wiley 2003). Two lower-level books with more basic explanations and applications to help you "make sense of it all". Useful if you already have them, but don't buy just for this class (you can always go to the library).
  5. C. Cohen-Tannoudji, B. Diu, F. LaloŽ: "Quantum Mechanics" Volumes 1 and 2, Wiley. The most comprehensive tome, but somewhat hard to read. For people who think this class is too easy! ;-)
  6. JJ. Sakurai: "Modern Quantum Mechanics" Revised Edition, Addison Wesley 1994. Relatively compact but intense.

Recommended Lecture Notes

Dr. W. van Orden's Lecture Notes on Quantum Mechanics (priceless!)

Syllabus and Schedule

Preliminary schedule of topics, linked to page numbers in R. Shankar's book


Collection of useful formulae and relationships

News and Announcements

I have posted (under Useful Links) a replica of the page with Clebsch-Gordan coefficients for your viewing pleasure.

Make sure you attend all colloquia - it's part of your "course load" (and, more importantly, your education as a Physicist).

Lecture Notes

  1. 1st lecture (Statistics and ensembles of particles)
  2. 2nd lecture (Density matrix)
  3. 3rd lecture (Multi-particle states)
  4. 4th lecture (Entanglement)
  5. 5th lecture (Bosons and Fermions)
  6. 6th lecture (Bosons and Fermions)
  7. 7th lecture (Bosons and Fermions)
  8. 8th lecture (Tensor Operators, Wigner-Eckart Theorem)
  9. 9th lecture (Classical Limit: Particle-Wave-Fluid)
  10. 10th lecture (Classical Limit: Wave-Fluid and Wigner Function)
  11. 11th lecture (Classical Limit: WKB method)
  12. 12th lecture (Path integral formalism)
  13. 13th lecture (Path integral formalism + Variational Method)
  14. 14h lecture (Variational Method)
  15. 15th lecture (Time-independent Perturbation Theory)
  16. 16th lecture (Time-independent Perturbation Theory II); see also our Recitation Session of March 22
  17. 17th lecture (Time-independent Perturbation Theory III)
  18. 18th lecture (Time-dependent Perturbation Theory I) (really covers 1 1/2 lectures); supplemental material (higher order Time-dep. PT)
  19. 19th lecture (Time-dependent Perturbation Theory II) (really covers 1 1/2 lectures)
  20. 20th lecture (Time-dependent Perturbation Theory III)
  21. 21st lecture (Scattering Theory I - 1D)
  22. 22nd lecture (Scattering Theory II - Phase Shifts); see also my 2-page overview of scattering theory in general
  23. 23nd lecture (Scattering Theory III - Born Approximation)
Tying it all together: Relativistic elastic scattering (Recitation Friday 4/27)


Useful Links

The following PDF File contains all Clebsch-Gordan coefficients you'll ever need (and even things like Ylm's and rotational matrices dmm'!). Note that what's given is <j1j2m1m2|JM>, where j1 x j2 is indicated at the top left corner of every "mini-table", J and M are on top of each other as column labels and m1 and m2 are next to each other as row labels. Be careful to put a square root over each of the fractions, and of keeping track of minus signs: <j1j2 m1m2|JM> = <JM|j1j2 m1m2>, but if you interchange j1 and j2 (as you must if your j2 is larger than your j1), you get a total minus sign if J - j1 - j2 is odd! Finally, here is the Wigner-Eckard Theorem: <a,j',m'|Tkq|a,j,m> = <a,j'||Tkq||a,j><j'm'|kj qm>.

I made a little page with pictures of spherical Harmonics and spherical Bessel functions (partially stolen from )

Some more "quantum links" of potential interest:

A collection of QM-related tutorials, animations, notebooks...:

A special edition of Physics World - a lot about QM in the middle section.

Is Heisenberg's uncertainty principle under siege? Not really...

A somewhat unusual approach to teaching quantum mechanism - [viewer discretion advised]

The Pauli principle "reloaded"

A light-hearted look at what "expert quantum physicists" think about the meaning of it all: - here is a simplified writeup.

Two entangled particles not exciting enough? How about eight?

Physics World's list of the 10 greatest discoveries of 2011 - at least 4 are directly related to Quantum Mechanics:

Take a look at - relating to the "molecular cloud picture" of QM wave functions (and the classical limit)...

A new take on particle-wave duality

Here is a link to the classical paper by Aharonov and Bohm on the "ghostly" effect of the vector potential on the wave function of an electron.

...and here is a thoroughly amusing (unintentionally so) example of "quantum quackery". Warning: Don't sign up or take anything on this site seriously!

On the other hand, this discussion is more serious and challenging: