Classical and Quantum Dynamics From Classical Paths to Path Integrals /

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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Dittrich, Walter (Autor), Reuter, Martin (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edición:4th ed. 2016.
Colección:Graduate Texts in Physics,
Temas:
Quantum physics.
Physics.
Mathematical physics.
Nuclear physics.
Quantum Physics.
Classical and Continuum Physics.
Mathematical Physics.
Nuclear and Particle Physics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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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