Honours Quantum Mechanics (Fall 2011)
A generally ambitious outline of which we may or may not cover in toto.
- Postulates of QM, mathematics of QM, infinite dimensinal vector spaces. Functions as vectors. Hermitian vs. Self-Adjoint. Spectral decomposition. Lie Algebra. Generators of transformations. Representation Theory. Uncertainty relations.
- Time independent QM. Time dependent QM: Heisenberg Picture, Schroedinger picture.
- Feynman Path Integrals. Trotter formula. Propagator for a free particle, the simple harmonic oscillator, a linear potential. Functional analysis.
- Perturbation Theory. Time independent: nondegenerate and degenerate. Time dependent: time ordered exponential, Dyson series. Interaction picture.
- Scattering Theory. Lippmann-Schwinger equation. Fermi's Golden Rule. Born cross-section. Decomposition of the resolvent. Breit-Wigner distribution. Optical theorem.
- Bell's Inequality and the EPR paradox
- Quantum Statistics. Bosons vs. fermions
- Density Matrices
- WKB approximation
- Method of Steepest Descent
We won't be following any one particular book, but we will likely cleave closest to Shankar. Here are some suggestions of books to read for learning quantum mechanics.
- J. J. Sakurai, Modern Quantum Mechanics, Addison Wesley, 2010.
- R. Shankar, Principles of Quantum Mechanics, Springer, 1994.
- A. Messiah, Quantum Mechanics, Dover, 1999.
- R. L. Liboff, Introductory Quantum Mechanics, Addison Wesley, 2002.
- F. Schwabl, Quantum Mechanics, Springer, 2010.
Griffith's is also a useful resource.
- (Possibly) useful online notes on quantum mechanics can be found here and here; Professor Littlejohn's notes seem especially helpful, found here.
- (Possibly) useful hardcopy notes on QM can be found here and here.
- (Possibly) useful hardcopy notes on Green's functions can be found here.
- A very nice exposition on dealing rigorously with the mathematics of infinite dimensional vector spaces can be found here.
- Set #0, due Tuesday, February 15th.
- Set #1, due Tuesday, February 22nd.
- Set #2, due Tuesday, March 1st.
- Set #3, due Tuesday, March 8th.
- Set #4, due Tuesday, March 15th.
- Set #5, due Tuesday, April 12th.
- Set #6, due Tuesday, April 19th.
- Set #7, due Tuesday, May 3rd.
- Set #8, due Tuesday, May 10th.
- Set #9, due Tuesday, May 17th.