A Brief Introduction to Classical, Statistical, and Quantum Mechanics

This book provides a rapid overview of the basic
methods and concepts in mechanics for beginning Ph.D. students and
advanced undergraduates in applied mathematics or related fields. It is
based on a graduate course given in 2006-07 at the Courant Institute
of Mathematical Sciences. Among other topics, the book introduces
Newton's law, action principles, Hamilton-Jacobi theory, geometric wave
theory, analytical and numerical statistical mechanics, discrete and
continuous quantum mechanics, and quantum path-integral methods.

The
focus is on fundamental mathematical methods that provide connections
between seemingly unrelated subjects. An example is Hamilton-Jacobi
theory, which appears in the calculus of variations, in Fermat's
principle of classical mechanics, and in the geometric theory of
dispersive wavetrains. The material is developed in a sequence of
simple examples and the book can be used in a one-semester class on
classical, statistical, and quantum mechanics. Some familiarity with
differential equations is required but otherwise the book is
self-contained. In particular, no previous knowledge of physics is
assumed.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.