These lecture notes comprise a three-semester graduate course in quantum mechanics at the University of Illinois. There are a number of texts which present the basic topics very well; but since a fair quantity of the material discussed in my course was not available to the students in elementary quantum mechanics books, I was asked to prepare written notes. In retrospect these lecture notes seemed sufficiently interesting to warrant their publication in this format. The notes, presented here in slightly revised form, consitutute a self-contained course in quantum mechanics from first principles to elementary and relativistic one-particle mechanics. Prerequisite to reading these notes is some familiarity with elementary quantum mechanics, at least at the undergraduate level. Preferably the reader should already have met the uncertainty principle and the concept of a wave function. Prerequisites also include sufficient acquaintance with complex cariables to be able to do simple contour integrals and to understand words such as "poles" and "branch cuts." An elementary knowledge of Fourier transforms and series is necessary. I also assume an awareness of classical electrodynamics.

* Photon Polarization * Neutral K Mesons * The Motion of Particles in Quantum Mechanics * Potential Problems, Mostly in One Dimension * Equations of Motion for Operators * Orbital Angular Momentum and Central Potentials * The Hydrogen Atom * Cooper Pairs * Potential Scattering * Coulomb Scattering * Stationary State Perturbation Theory * Time-Dependent Perturbation Theory * Interaction of Radiation with Matter * Spin 1/2 * Addition of Angular Momenta * Isotopic Spin * Rotations and Tensor Operators * Identical Particles * Second Quantization * Atoms * Molecules * Relavistic Spin Zero Particles: Klein-Gordon Equation * Relavistic Spin 1/2 Particles: Dirac Equation