Graduate Texts in Physics / Classical and Quantum Dynamics

Introduction.- The Action Principles in Mechanics.- The Action Principle in Classical Electrodynamics.- Application of the Action Principles.- Jacobi Fields, Conjugate Points.-Canonical Transformations.- The Hamilton-Jacobi Equation.- Action-Angle Variables.- The Adiabatic Invariance of the Action Variables.- Time-Independent Canonical Perturbation Theory .- Canonical Perturbation Theory with Several Degrees of Freedom.- Canonical Adiabatic Theory.- Removal of Resonances.- Superconvergent Perturbation Theory, KAM Theorem.- Poincaré Surface of Sections, Mappings.- The KAM Theorem.- Fundamental Principles of Quantum Mechanics.- Functional Derivative Approach.- Examples for Calculating Path Integrals.- Direct Evaluation of Path Integrals.- Linear Oscillator with Time-Dependent Frequency.- Propagators for Particles in an External Magnetic Field.- Simple Applications of Propagator Functions.- The WKB Approximation.- Computing the trace.- Partition Function for the Harmonic Oscillator.- Introduction to Homotopy Theory.- Classical Chern-Simons Mechanics.- Semiclassical Quantization.- The "Maslov Anomaly" for the Harmonic Oscillator.-Maslov Anomaly and the Morse Index Theorem.- Berry's Phase.- Classical Analogues to Berry's Phase.- Berry Phase and Parametric Harmonic Oscillator.- Topological Phases in Planar Electrodynamics.- Appendix.- Solutions.- Index.

Prof. Walter Dittrich, Tübingen, Germany

Prof. Martin Reuter, Mainz, Germany

"This is the fourth edition of a highly successful pedagogical book that combines classical and quantum dynamics, often viewed as disjoint subjects. ... Its elementary exposition makes the book accessible to graduate students." (Gert Roepstorff, zbMATH 1330.81001, 2016)