Walter Dittrich & Martin Reuter 
Classical and Quantum Dynamics [PDF ebook] 
from Classical Paths to Path Integrals

In the past 10 to 15 years, the quantum leap inunderstanding of nonlinear dynamics has radically changedthe frame of reference of physicists contemplating suchsystems. This book treats classical and quantum mechanicsusing an approach as introduced by nonlinear Hamiltoniandynamics and path integral methods. It is written forgraduate students who want to become familiar with the moreadvancedcomputational strategies in classical and quantumdynamics. Therefore, worked examples comprise a large partof the text. While the first half of the book lays thegroundwork for a standard course, the second half, with itsdetailed treatment of the time-dependent oscillator, classical and quantum Chern-Simons mechanics, the Maslovanomaly and the Berry phase, willacquaint the reader withmodern topological methods that have not as yet found theirway into the textbook literature.