Physics 721: Advanced Quantum Mechanics
Fall 2006

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: 757-272-2697
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:

Problem sets:

Problem sets will generally be due on Tuesdays.

Problem Set 1 (ps, pdf), due Tuesday, September 19.
Problem Set 2 (ps, pdf), due Tuesday, September 26.
Problem Set 3 (ps, pdf), due Tuesday, October 10.
Problem Set 4 (ps, pdf), due Tuesday, October 24.
Problem Set 5 (ps, pdf), due Tuesday, November 7.
Problem Set 6 (ps, pdf), due Thursday, November 30 -- postponed to December 7.
Problem Set 7 (ps, pdf), due Thursday, December 7.

Midterm Exam:

(midterm.ps, midterm.pdf)

Questions about the midterm exam:
Questions received during the exam will be answered here.

1) In part (b) is epsilon a function of the three-vector k or the four-vector k?
For solutions to the equations of motion k_0 is a function of the three-vector k, right? (Actually, this is a little too quick -- Any polarization 4-vector can be decomposed into a longitudinal and a transverse part. As you will show in parts (c) and (d), for each of these modes the polarization 4-vector and the momentum 4-vector depend only on the spatial momentum 3-vector.)

2) In part (d) are we also supposed to assume that the polarization 4-vector is proportional to k as in part (c)?
No.

3) When you say that the momentum conjugate to A_0 vanishes does that mean I should ignore d_a A_0?
No, I mean the canonical momentum conjugate to A_0 vanishes, but you do not need to impose a commutation relation [A_0,Pi_A0]=...

4) For part (j) should we use the results of part (i)?
Yes. Later parts of the exam may depend on results of earlier parts, so you should at least look at what is to be shown in the optional parts before skipping them.

5) What do you want us to do in part (g)?
A few of you have asked me about this part, probably because you're not expecting anything so trivial. I just want to see that you know what it means to canonically quantize a field theory.

6) In part (i) how can we show that the completeness relation is satisfied just by using the rest frame, when the completeness relation is a function of the three-vector k?
I'm not asking you to show the k-dependence. Just show that it is satisfied in the rest frame.

7) In part (j) what do you mean by Jtilde(-omega_k3,-k3)?
I mean Jtilde is a function of the 4-vector k^mu=(-omega_k3,0,0,-k3).

Final Exam:

(final.ps, final.pdf)

Questions about the final exam:
Questions received during the exam will be answered here.

1) What are non-spacetime symmetries?
They are symmetries not involving transformations of the spacetime coordinates, i.e. NOT spacetime translations, rotations, Lorentz boosts, etc.

2) In 2b and 2d, do you want the potentials in position space or momentum space?
Evaluate the nonrelativistic potential, V(r), in position space, as we did for the Coulomb potential. Identify the term in the scattering amplitude corresponding to the exchange potential, which may be left in momentum space.

3) In 2d, do you mean for us to consider elastic scattering of nucleons and antinucleons?
Yes, I mean scattering of a nucleon and antinucleon into a nucleon and antinucleon. That is what is relevant for the calculation of the potential.

4) In 2b and 2d are we supposed to take the nonrelativistic limit?
Yep.

5) In 1f how do you make the muons in an eigenstate of chirality if they are massive?
Good question! Chirality eigenstates are not Hamiltonian eigenstates in the free theory for massive fermions. Part 1f doesn't really make sense, and if you noticed it yourself then good for you!