Graduate Quantum Mechanics I

Welcome to the Physics 389K class, Graduate Quantum Mechanics (I).

In the Fall of 1996, this course is taught by:

Course Content

Basic Physical and Mathematical Concepts of QM:

Quantum states and the Hilbert space; observables, operators, bases and matrices; commutation relations and uncertainty rules; momentum and space translations; density matrices*.

Quantum Dynamics:

Schrödinger and Heisenberg-Dirac equations; canonical quantization; quantization of the harmonic oscillator and the creation/annihilation operators; lasers.

Wave Mechanics:

Bound and unbound states; reflection, tunneling and scattering; semi-classical WKB approximation; coupling to electromagnetic fields and gauge invariance; Aharonov-Bohm effect, SQUIDs and magnetic monopoles*.

Rotations and Angular Momentum:

Rotations and the J operator; commutation relations and the spectrum of the angular momentum; representations, spin and the SU(2) group; orbital angular momentum and the central potential; adding angular momenta and Clebbsch-Gordan coefficients; tensors and Wigner-Eckart theorem; general continuous symmetries -- groups, generators, commutation relations and representations*; parity and other discrete symmetries.

Perturbation Theory:

Time-independent perturbations, non-degenerate and degenerate; fine structure; Born-Oppenheimer theory of molecules*; time-dependent perturbations and quantum transitions*; Fermi's Golden rule*.

In case of a class that needs stronger coverage of basic subjects (or if time is too short for any other reason), the subjects marked with a* would be sacrificed.

Textbook

The main textbook for this course is Modern Quantum Mechanics by J. J. Sakurai; the first five chapters of this book cover 90% of the course material. I also recomment Quantum Mechanics by A. S. Davydov as a supplementary textbook; it's somewhat old-fashioned but very solid and covers many subjects not covered by Sakurai, in particular undergraduate-level subjects such as hydrogen atom, but also advanced subjects such as superconductivity. There are many other well-known QM textbooks you might find useful; check them in the library before buying.

Homeworks, Exams and Grades

The grades for this course will be based on homeworks (50%) and the final exam at the end of the semester (50%). The final exam will be comprehensive; there will be no mid-term tests.

Generally, the homeworks will be assigned weekly and will be due a week later. Be warned: The homeworks will be very hard. If you start working on an assignment the day before it's due, you will not finish it in time.

Homeworks are essential for understanding the course material. Often, due to the time pressure, I will explain the general theory in class and leave the examples for the homework assignment; if you do not work them out by yourself, you would not really understand what I was talking about in class!