Instructor: Omer Blaes
Office Hours:
| Monday | 2:00-3:00 PM | in Broida 2015G |
| Thursday | 1:00-3:00 PM | in Broida 2015G |
| Friday | 1:00-2:00 PM | in Broida 2015G |
Teaching Assistant: Miles Stoudenmire
Office Hours:
| Tuesday | 3:30-5:00 PM | in Physics Study Center | |
| Thursday | 2:00-3:30 PM | in Physics Study Center |
Announcements:
Quantum mechanics is perhaps the most conceptually challenging branch of modern physics, with both physicists and philosophers continuing to argue about what it really means for the nature of reality. However, it also has concrete applications to widely diverse fields in physics, from astrophysics to high energy physics, and is at the heart of some of the most interesting experimental challenges today, including nanotechnology and quantum computing.
This course should give you a fairly thorough and advanced treatment of nonrelativistic quantum mechanics, although we will be doing some basic relativistic quantum mechanics in the third quarter. Every physicist worthy of the name should have some familiarity with the material in this course.
J. J. Sakurai, Modern Quantum Mechanics, 2nd edition (Addison-Wesley, 1994).
We will be using Sakurai as our primary reference for the first two and a bit quarters of the course. (Much of the last quarter will be devoted to some more advanced topics, including relativistic quantum mechanics, group theoretical techniques, and a variety of practical applications.)
There are many good books out there on quantum mechanics at approximately the right level for this course. In addition to Sakurai, I have also placed the following books on reserve in the library:
G. Baym, Lectures on Quantum Mechanics
L. D. Landau & E. M. Lifshitz, Quantum Mechanics (Non-relativistic Theory), 3rd edition.
R. Shankar, Principles of Quantum Mechanics, 2nd edition.
L. I. Schiff, Quantum Mechanics, 3rd edition.
Baym's book is a great read, covering a variety of topics and unique applications in a very original fashion. Landau & Lifshitz is a good reference, but like other books in the Landau-Lifshitz series, it is difficult to learn the subject from just this source. While it covers some topics much better than Sakurai, it is also missing other topics entirely. Shankar is an extremely clear (if overly pedantic) presentation of many of the mathematical aspects of the subject, and I highly recommend that you consult it on aspects of the course that you find mathematically confusing. Finally, Schiff is the book that I and many of my generation learned the subject from. It's very elegant, but it is also extremely concise and can be difficult for the beginner. Schiff is also a bit out of date and doesn't cover all the topics that are necessary for a modern course in the subject.
You may find the following web resources useful (let me know if you discover any more):
Finally, as an additional resource, I intend to post weekly copies of my lecture notes.
You should have already completed a one year course in quantum mechanics at the upper division undergraduate level, and be very familiar with the position-dependent wave function form of Schrodinger's equation. If you have mastered the material presented in Griffiths, Introduction to Quantum Mechanics, you should be fine. It is also important that you be familiar with abstract vector spaces and linear algebra, special functions (in particular spherical harmonics and Legendre polynomials), Fourier transforms and delta functions, and the use of the residue theorem to calculate integrals. The book by Arfken, Mathematical Methods for Physicists, covers these topics at an adequate depth for this course. I have also placed both Griffiths and Arfken on reserve in the library should you need to consult them.
Homework (50% of final grade): One assignment will be due on Fridays each week.
Final Exam (50% of final grade): The final exam will be a 24 hour take home exam, and will be due at noon on Friday, June 13.
The following schedule is probably too ambitious, and I suspect that I will end up going a bit slower. All reading assignments are from Sakurai.
| Week | Date | Topic | Reading Assignment | |
| 1 | M | 3/31 | Permutation Symmetry, Bosons and Fermions | 6.1, 6.2 |
| W | 4/2 | Two Electron Systems | 6.3 | |
| F | 4/4 | The Helium Atom | 6.4 | |
| 2 | M | 4/7 | Young Tableaux | 6.5 |
| W | 4/9 | Second Quantization | --- | |
| F | 4/11 | Second Quantization (cont.) | --- | |
| 3 | M | 4/14 | Scattering and The Lippmann-Schwinger Equation | 7.1 |
| W | 4/16 | The Born Approximation | 7.2 | |
| F | 4/18 | The Optical Theorem | 7.3 | |
| 4 | M | 4/21 | The Eikonal Approximation | 7.4 |
| W | 4/23 | Plane Wave and Spherical Wave Free Particle States | 7.5 | |
| F | 4/25 | Method of Partial Waves | 7.6 | |
| 5 | M | 4/28 | Hard Sphere Scattering | 7.6 |
| W | 4/30 | Low Energy Scattering and Bound States | 7.7 | |
| F | 5/2 | Resonance Scattering | 7.8 | |
| 6 | M | 5/5 | Identical Particles and Scattering | 7.9 |
| W | 5/7 | Symmetry in Scattering | 7.10 | |
| F | 5/9 | Time Dependent Formulation of Scattering | 7.11 | |
| 7 | M | 5/12 | Inelastic Electron-Atom Scattering | 7.12 |
| W | 5/14 | Coulomb Scattering | 7.13 | |
| F | 5/16 | The Adiabatic Theorem and Berry's Phase | pp. 464-470 | |
| 8 | M | 5/19 | Aharonov-Bohm Effect Revisited | pp. 471-474 |
| W | 5/21 | The Dynamical Jahn-Teller Effect | pp. 475-480 | |
| F | 5/23 | The Dirac Equation | --- | |
| 9 | M | 5/26 | Memorial Day | --- |
| W | 5/28 | The Dirac Equation (cont.) | --- | |
| F | 5/30 | Measurement and Decoherence | --- | |
| 10 | M | 6/2 | Measurement and Decoherence | --- |
| W | 6/4 | Measurement and Decoherence | --- | |
| F | 6/6 | Measurement and Decoherence | --- | |
|
|
||||
| Thursday | 6/12 | FINAL EXAM | ||