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,...
Κύριοι συγγραφείς: | , |
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Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2016.
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Έκδοση: | 4th ed. 2016. |
Σειρά: | Graduate Texts in Physics,
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Θέματα: | |
Διαθέσιμο Online: | Full Text via HEAL-Link |
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 Analogues to Berry’s Phase
- Berry Phase and Parametric Harmonic Oscillator
- Topological Phases in Planar Electrodynamics
- Appendix
- Solutions
- Index.