Course Identification

This is a seminar course on advanced topics in classical and semiclassical mechanics. The course will meet once a week for 2 hours.  The format of the course will be approximately 50% frontal lectures by the instructor and 50% seminars by the students on topics that are part of the syllabus.

I. Classical Mechanics

                A. The Lagrangian and the action

                B. Canonical transformations

                C. Time evolution in phase space

                D. Classical resonance theory

                E. Periodic orbits

                F. Geometrical approach to classical mechanics

II. Semiclassical Mechanics

                A. Feynman path integration

                B. The semiclassical propagator (van Vleck-Gutzwiller propagator)

                C. Gutzwiller trace formula

                D. Phase space representations of wavefunctions and densities

                E. The semiclassical coherent state propagator

                F. Initial value representations and Gaussian wavepacket methods

                G. WKB methods

The student will learn a variety of advanced topics in classical mechanics and then how these reformulations of classical mechanics lead to quantum mechanics and semiclassical approximations.

The primary text will be The Semiclassical Way by Heller. Additional texts: Gutzwiller, Chaos in Classical and Quantum Mechanics; Arnold, Geometrical Methods in Classical Mechanics; Miller, Classical S-matrix Theory.