Classical and Quantum Dynamics [E-Book] : 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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Full text |
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Personal Name(s): | Dittrich, Walter, author |
Reuter, Martin, author | |
Edition: |
4th ed. 2016. |
Imprint: |
Cham :
Springer,
2016
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Physical Description: |
XIV, 461 pages 2 illustrations (online resource) |
Note: |
englisch |
ISBN: |
9783319216775 |
DOI: |
10.1007/978-3-319-21677-5 |
Series Title: |
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Graduate Texts in Physics
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Subject (LOC): |
- 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.