Physics 53 (Advanced Quantum Mechanics) Home Page, Fall 2004

Physics 53: Advanced Quantum Mechanics


09/26/04 Problem set 3 and the latest talk topics are posted below. I have continued to add to the list of suggested papers, as well. If there's a subject that you are interested in that's not on the list, ask me and I can help you find a paper that you might be able to talk about.

09/18/04 I've added problem set 2 below. Sorry I forgot to do this before now.

09/13/04 I've added some papers to the list of interesting papers below. Some of them may be appropriate for Monday talks. I'll keep adding to the list.

09/13/04 The problem set due Wednesday is from Griffiths, 2nd. edition. Unfortunately, the problems are different in the first edition (which you all have). I'll photocopy the problems and bring them to class today. In the future I'll either hand out the problems or assign them from the first edition. Sorry for any inconvenience.

09/13/04 You may find it useful to use mathematica for some of the problems in the problem sets this semester. I've added some links to mathematica tutorials in case you're not familiar with mathematica.

09/02/04 The course is tentatively scheduled for MW 2:00-3:20 in Merrill 204. This is subject to negotiation at the first meeting (on Wed. Sept. 8).

08/10/04 I've selected the textbook for the course. It should be available at the Jeffrey Amherst Bookshop soon.


Course Information

Course Description (from the course catalog)

This course is a continuation of Physics 48. We will study variational methods, semiclassical approximations, time-dependent perturbation theory, nonrelativistic scattering theory, and the quantization of the radiation field. Three hours per week.

Schedule Times and places:


Physics 48 or consent of the instructor

Course requirements

Statement of Intellectual Responsibility: particulars for this course

How to get the most from this class:



Required (should be available at the Jeffrey Amherst bookstore): I've asked the library to order copies of these books. They'll be placed on reserve when they arrive.

Additional useful references (if the library doesn't have them, I'll try to get them):

On quantum mechanics in general: Math books:

Key derivations / chains of logic / results to commit to memory

Mathematica Tutorials

We will use Mathematica 5.0 at least occasionally in the homework, to obtain numerical solutions to problems that are not analytically solvable and to simplify plotting of results. If you've never used Mathematica before, or haven't used it much, the tutorials will help you get started. They were written by Professor Hilborn and revised by Rebecca Erwin '02. If you download the file and save it to the desktop with a .nb suffix in the name, your computer will recognize it as a Mathematica notebook and will start up Mathematica automatically when you double-click on the icon, provided you have Mathematica installed. Mathematica is installed on lots of the college's public machines, including on the computers in the Physics Department computer lab. Alternately, you can pay the $140 or so to buy the student version.

Lecture Schedule
Week Notes Hmwk
1. September 6 Variational Principles in QM

Sept 8: Introduction to the course / Variational principle
General course information. Variational principles in QM.

Read: Griffiths, Chap 7: Variational Principles
Problems: Griffiths (2nd ed), 7.4, 7.7, 7.10, 7.14, 7.15, 7.16, 7.18, 7.19, 7.20

2. September 13 Variational Principles and Scattering

Sept 13: Variational Principle
[Handout: sections of Schaum's QM, for review]

Sept 15: Scattering

Read: Griffiths, Sec. 2.5-2.6 (review discussion of scattering)
Problems: Griffiths (1st ed.), 2.27, 2.32, 2.34, 2.35, 2.48, 2.49

3. September 20 1D Scattering

Sept 20 (morning): Talks

Maggie McKeon:
Neutron stars for undergraduates

Tarun Menon:
Tunneling ionization of atoms

Sept 20 (afternoon): 1D scattering

Sept 22: More 1D scattering

Read: Griffiths, Chap 11 (scattering)
Problems: Griffiths (1st ed.): 11.1 (as Griffiths suggests, seek help from a mechanics book with this one), 11.2, 11.6, 11.10, 11.12, 11.13, 11.14, 11.15

4. September 27 3D Scattering

Sept 27 (morning): Talks

Nathaniel Reden:
Energy conservation in quantum mechanics

Ben Heidenreich:
Schiff's Theorem

Sept 27 (afternoon): 3D scattering

Sept 29: More 3D scattering

Read: Griffiths, Chap 11 (scattering)
Problems: Griffiths (1st ed.): 11.3, 11.4, 11.7, 11.8 (short one this week)

5. October 4 TBA

Oct 4 (morning): Talks

Tarun Menon:
Bose-Einstein condensation in the alkali gases: Some fundamental concepts (about first 10 pages)

Maggie McKeon:
A remarkable mathematical property of the Lande factor in quantum mechanics

Oct 4 (afternoon):

Oct 6:

6. October 11 TBA

Oct 11: Fall Break

Oct 13:

7. October 18 TBA

Oct 18 (morning): Talks

Nathaniel Reden:
What is a state in quantum mechanics?
American Journal of Physics, Vol. 72, No. 3, pp. 348-350, March 2004

Oct 18 (afternoon):

Oct 20:

8. October 25 TBA

Oct 25 (morning): Talks

Maggie McKeon:

Tarun Menon:
Bose-Einstein condensation in the alkali gases: Some fundamental concepts (about pages 10-20)

My talk is going to be based on the same Legget paper I talked about last time. This time, IÕll be covering material from pages 10-20. I am going to be talking about the effect of inter-atomic interactions in a Bose-Einstein Condensate. I will talk about the Gross-Pitaevskii approximation that describes these interactions. I am also hoping to include some of the work we have been doing in the lab on tunable interactions. To this end I will be talking about Feshbach resonances. I couldnÕt track down an appropriate paper, but IÕll try to keep it simple, and hopefully the fact that weÕve just covered scattering theory will help. I will also talk about phase separation in double condensates.

Oct 25 (afternoon):

Oct 27:

9. November 1 TBA

Nov 1 (morning): Talks

Nathaniel Reden:
Neutrino physics: An update
American Journal of Physics, Vol. 72, No. 1, pp. 18-24, Jan. 2004

The paper is mostly particle physics, and not explicitly quantum mechanics, but I will attempt to build a quantum mechanical framework for the neutrino at the beginning of the talk, during which I will discuss the background to neutrino physics. We will examine the three flavors of neutrino and the neutrino mass(es). From there I will move on to the Sudbury Neutrino Observatory experiment, and talk about how the measurements taken there differ from those taken at the SuperKamiokande detector. If there is time I will attempt to discuss the KamLAND experiment as well.

Nov 1 (afternoon):

Nov 3:

10. November 8 TBA

Nov 8 (morning): Talks

Maggie McKeon:
Anomalies in quantum mechanics: the inverse-squared potential
American Journal of Physics, Vol. 70, No. 5, pp. 513-519, May 2002.

This paper looks at potentials that give rise to a classical valid symmetry that is broken due to quantization. The 1/r^2 potential is a specific example that the paper discusses, along with some experimental consequences.

Tarun Menon:
Quantum Mechanics Helps in Searching for a Needle in a Haystack
PRL 79, 325-328 (1997)

My talk will be on Grover's search algorithm. It is a quantum algorithm designed to solve problems such as searching a database for a particular telephone number. It allows us to perform this process in a fewer number of steps than the most efficient classical algorithm, and really illustrates the power of quantum computing. It could be particularly effective in cryptanalysis, allowing us to search a large number of keys in a fraction of the time required now.

Nov 8 (afternoon):

Nov 10:

Read: Townsend section
Problems: Townsend, 14.3, 14.4, 14.5, 14.6, 14.7
14. December 9 TBA

Dec 9:
Dec 10: (Last day)
Dec 11: Reading period
Dec 13: Reading period
Finals week Final exam: TBA


I'll keep scheduling information on this site primarily. I may occasionally use Blackboard as well.

Useful Links

I'll post interesting or useful links pertinent to the course here as they I come across them. If you come across any others, please let me know.

Interesting talks in the Five-College area:

You should start attending the departmental colloquia early and often. They are intended primarily for you, to broaden your exposure to current physics in ways that the department faculty alone cannot. They'll give you an overview of what exciting work is going on in physics and who's doing it. In the beginning you won't always understand all of the talks, but you'll be surprised by how much you can understand even now. In addition, the colloquium food here is better than anywhere else I've ever been. Plus, I organize the colloquia, and it warms my heart to see you there.

Area Seminars and colloquia

Interesting and useful papers:

Here are some papers that may be good to talk about for your Monday talks. Not all papers are necessarily appropriate (they're here primarily because the title looked to me somewhat quantum-mechanical), and just because they're listed here doesn't mean you don't have to check them with me. But this list is a good place to start looking.

Interesting and useful websites: