Classical & quantum dynamics

Contents

• 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-Independant Canonical Perturbation Theory
• Canonical Perturbation Theory with Several Degrees of Freedom
• Canonical Adiabatic Theory
• Removal of Resonances
• Superconvergent Perturbation Theory, KAM Theorem (Introduction)
• Poincaré Surface of Sections, Mappings
• The KAM Theorem
• Fo,damental 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 au External Magnetic Field
• Simple Applications of Propagator Functions
• The WXB Approximation
• Computing the trace
• Partition Function for the Harmonie Oscillator
• Introduction to Homotopy Theory
• Classical Chern-Simons Mechanics
• Semiclassical Quantization
• The "Maslov Anormaly" for the Harmonic Oscillator
• Maslov Anormaly 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
• References
• Index