Classical and Quantum Dynamics From Classical Paths to Path Integrals

Classical and Quantum Dynamics From Classical Paths to Path Integrals / by Walter Dittrich, Martin Reuter.

Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase,...

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Bibliographic Details
Main Authors: Dittrich, Walter (Author), Reuter, Martin (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edition:4th ed. 2016.
Series:Graduate Texts in Physics,
Springer eBook Collection.
Subjects:
Quantum physics.
Continuum physics.
Mathematical physics.
Nuclear physics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of 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-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.

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