Physics 721: Advanced Quantum Mechanics
Fall 2005

Class schedule: T,Th 9:30-10:50am, Small Hall, Room 102
Office hours: By arrangement or any time instructor is in office

Instructor - Josh Erlich
Small Hall, Room 220
Office Phone: 757-221-3763
Cell Phone: 425-876-5171
Email: erlich@physics.wm.edu

Topics to be covered:

Examples will be taken from atomic, condensed matter, and particle physics.

Course requirements and grade:

Reading material:

Midterm exam:

(midterm.ps, midterm.pdf), due 9:30am Tuesday, October 18.

Answers to questions asked during exam:
1) What do you mean theta is constant in part (8)?
I meant that theta is a parameter independent of the spacetime coordinates. I have reworded it in the exam if you click above.
2) What does the tilde on m-tilde mean?
The tilde is just meant to distinguish m-tilde from m. They are both constants with the dimension of mass.
3) On the page of useful information, the expression for sigma^(0i) is confusing because of the factor of i.
I have changed it to sigma^(0k). There was also a missing minus sign.
4) I'm finding that the Lagrangian density is not Lorentz invariant. Are you sure that it is?
Yes, I'm sure. By Lorentz invariant I mean that it is a Lorentz scalar, so to be precise it transforms into itself at the same point, i.e. L[phi(x)] -> L[phi(Lambda^(-1)(x))]. Then the action is truly invariant.
5) What do you mean in part (3) when you say to check that the eqs are consistent?
I mean that the eqs (by varying with respect to psi and psi-bar) should be Hermitian conjugates of one another, perhaps up to multiplication by a gamma matrix.

Final exam:

(final.ps, final.pdf), due 9:30am Tuesday, November 22.

I have included two pages from Griffith's particle physics book to help with gamma matrix traces, but only in the hardcopy version of the exam. It is the same information as in Section 5.1 of Peskin and Schroeder. I will leave them outside room 221.

Good luck!

Answers to questions asked during exam:
1) In problem 2, do you mean scattering of electrons or scattering of one electron?
I mean scattering of a beam of electrons by a Coulomb field. I do not mean scattering of electrons off of one another, which does not happen in this theory because the electromagnetic field is not dynamical.
2) Is the amplitude the same as the scattering matrix element?
Yes it is.
3) Do we need to derive the Feynman rules in Problem 1?
No, you don't.
4) When you say to take the nonrelativistic limit what u(p,s) should we use?
It is easiest to use the nonrealtivistic solutions to the Dirac equation in the Dirac basis, like when we derived the gyromagnetic ratio of the electron.
5) I'm getting zero for the potential in Problem 1. Is that right?
You should keep the leading terms in the nonrelativistic expansion of the scattering amplitude.
6) In Parts 2e and 2f is the electron relativistic or nonrelativistic?
Relativistic. You can use the nonrelativistic limit as a check of your answer.
7) What do you mean by "2-component Pauli spin matrices" in Part 1d?
I meant that the xi's are 2-component Pauli spinors, as usual. The term "spin matrices" was a typo.

Problem sets:

Problem sets will generally be due on Tuesdays.

Problem Set 1 (ps1.ps, ps1.pdf), due Tuesday, September 13.
Problem Set 2 (ps2.ps, ps2.pdf), due Tuesday, September 20.
Problem Set 3 (ps3.ps, ps3.pdf), due Tuesday, September 27.
Problem Set 4 (ps4.ps, ps4.pdf), due Tuesday, October 4.
Problem Set 5 (ps5.ps, ps5.pdf), will not be graded.
Problem Set 6 (ps6.ps, ps6.pdf), due Tuesday, November 1.
Problem Set 7 (ps7.ps, ps7.pdf), due Tuesday, November 8.
Problem Set 8 (ps8.ps, ps8.pdf), due Thursday, November 17.