Classical and Quantum Dynamics From Classical Paths to Path Integrals /

• Κύριοι συγγραφείς: Dittrich, Walter (Συγγραφέας), Reuter, Martin (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Έκδοση: 5th ed. 2017.
• Θέματα: Physics.; Mathematical physics.; Quantum physics.; Nuclear physics.; Quantum Physics.; Classical and Continuum Physics.; Mathematical Applications in the Physical Sciences.; Particle and Nuclear Physics.

Graduate students who wish to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book 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...

Πίνακας περιεχομένων:

• 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 Geometric Phases: Foucault and Euler
• Berry Phase and Parametric Harmonic Oscillator
• Topological Phases in Planar Electrodynamics
• Path Integral Formulation of Quantum Electrodynamics
• Particle in Harmonic E-Field E(t) = Esinw0t; Schwinger-Fock Proper-Time Method
• The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics
• Appendix
• Solutions
• Index.