Advanced Topics in Quantum Mechanics

Path integral formulation of quantum mechanics and applications, including uses of instantons, introduction to the quantum theory of interacting systems - mostly at the level of the Hartree-Fock approximation, Berry's phases, band theory including the basics of quantum geometry, an overview of the basics of scattering theory, and the rudiments relativistic quantum mechanics including second quantization, the Dirac equation, and the nature of gauge theories. Prerequisites: Physics 131, familiarity with linear algebra and partial differential equations, and the basics of quantum statistical mechanics. Undergraduates register for PHYSICS 134 (4 units). Graduate students register for PHYSICS 234 (3 units).