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Path integrals in quantum mechanics, statistics, polymer physics, and financial markets /
"This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutio...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2009.
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| Edición: | 5th ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface to Fourth Edition; Preface; Preface to Third Edition; Preface to Second Edition; Preface to First Edition; Contents; List of Figures; List of Tables; 1 Fundamentals; 1.1 Classical Mechanics; 1.2 Relati vistic Mechanics in Curved Spacetime; l.3 Quantum Mechanics; 1.3.1 Bragg Reflections and Interference; 1.3.2 Matter Waves; 1.3.3 SchrOdinger Equation; 1.3.4 Particle Current Conservation; 1.4 Dirac's Bra-Ket Formalism.; 1.4.1 Basis Transformations; 1.4.2 Bracket Notation; 1.4.3 Continuum Limit; 1.4.4 Generalized Functions; 1.4.5 SchrOdinger Equation in Dirac Notation
- 1.4.6 Momentum States1.4.7 Incompleteness and Poisson's Summation Formula; 1.5 Obscrvables; 1.5.1 Uncertainty Relation.; 1.5.2 Density Matrix and Wigner Function.; 1.5.3 Generalization to Many Particles; 1.6 Time Evolution Operator; l.7 Properties of the Time Evolution Operator; 1.8 Heisenberg Picture of Quantum Mechanics; l.9 Interaction Picture and Perturbation Expansion; 1.10 Time Evolution Amplitude; 1.11 Fixed-Energy Amplitude; 1.12 Free-Particle Amplitudes.; 1.13 Quantum Mechanics of General Lagrangian Systems.; 1.14 Particle on the Surface of a Sphere; 1.15 Spinning Top
- 1.16 Scattering1. 16.1 Scattering Matrix; 1.16.2 Cross Section; 1.16.3 Born Approximation; 1. 16.4 Partial Wave Expansion and Eikonal Approximation; 1. 16.5 Scattering Amplitude from Time Evolution Amplitude; 1. 16.6 Lippmann-Schwinger Equation; 1.17 Classical and Quantum Statistics; 1. 17.1 Canonical Ensemble.; 1. 17.2 Grand-Canonical Ensemble; 1.18 Density of States and Ttacelog; Appendix l A Simple Time Evolution Operator.; Appendix I B Convergence of the Fresnel Integral; Appendix l C The Asymmetric Top; Notes and References.; 2 Path Integrals
- Elementary Properties and Simple Solutions
- 2.1 Path Integral Representation of Time Evolution Amplitudcs2.1.1 Sliced Time Evolution Amplitude.; 2.1.2 Zero-Hamiltonian Path Integral.; 2.1.3 SchrOdinger Equation for Time Evolution Amplitude; 2.1.4 Convergence of of the Time-Sliced Evolution Amplitude; 2.1.5 Time Evolution Amplitude in Momentum Space.; 2.1.6 Quantum-Mechanical Partition Function.; 2.1.7 Feynman's Configurat ion Space Pat h Integral; 2.2 Exact Solution for the Frec Particle; 2.2. 1 Direct Solution; 2.2.2 Fluctuations around the Classical Path; 2.2.3 Fluctuation Factor
- 2.2.4 Finite Slicing Properties of Free-Particle Amplitude.2.3 Exact Solution for Harmonic Oscillator; 2.3. 1 Fluctuations around the Classical Path.; 2.3.2 Fluctuation Factor; 2.3.3 The i7]-Prescription and Maslov-Morse Index; 2.3.4 Continuum Limit.; 2.3.5 Useful Fluctuation Formulas.; 2.3.6 Oscillator Amplitude on Finite Time Lattice; 2.4 Gelfand-Yaglom Formula.; 2.4. 1 Recursive Calculation of Fluctuation Detcrminant.; 2.4.2 Examples; 2.4.3 Calculation on Unsliced Time Axis; 2.4.4 D'Alembert's Construction; 2.4 .5 Another Simple Formula.; 2.4.6 Generalization t o D Dimensions