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1 | Introducing and Defining the Path Integral | 3 |
Appendix: The Trotter Product Formula | 9 | |
2 | Probabilities and Probability Amplitudes for Paths | 13 |
3 | Correspondence Limit for the Path Integral (Heuristic) | 16 |
Appendix: Useful Integrals | 20 | |
4 | Vector Potentials and Another Proof of the Path Integral Formula | 22 |
5 | The Ito Integral and Gauge Transformations | 27 |
6 | Doing the Integral: Free Particle and Quadratic Lagrangians | 31 |
Appendix: Exactness of the Sum over Classical Paths | 39 | |
7 | Properties of Green's Functions; the Feynman-Kac Formula | 42 |
8 | Functional Derivatives and Commutation Relations | 49 |
9 | Brownian Motion and the Wiener Integral; Kac's Proof | 53 |
10 | Perturbation, Theory and Feynman Diagrams | 65 |
11 | Asymptotic Analysis | 73 |
12 | The Calculus of Variations | 79 |
13 | The WKB Approximation and its Application to the Anharmonic Oscillator | 92 |
14 | Detailed Presentation of the WKB Approximation | 108 |
15 | WKB Near Caustics | 118 |
16 | Caustics and Uniform Asymptotic Approximations | 131 |
17 | The Phase of the Semiclassical Amplitude | 143 |
18 | The Semiclassical Propagator as a Function of Energy | 147 |
19 | Scattering Theory | 158 |
20 | Geometrical Optics | 164 |
21 | The Polaron | 170 |
22 | Spin and Related Matters | 182 |
23 | Path Integrals for Multiply Connected Spaces | 190 |
24 | Quantum Mechanics on Curved Spaces | 214 |
25 | Relativistic Propagators and Black Holes | 225 |
26 | Applications to Statistical Mechanics | 237 |
27 | Coherent State Representation | 242 |
28 | Systems with Random Impurities | 259 |
29 | Critical Droplets, Alias Instantons, and Metastability | 271 |
Appendix: Small Oscillations about the Instanton | 284 | |
30 | Renormalization and Scaling for Critical Phenomena | 290 |
31 | Phase Space Path Integral | 303 |
32 | Omissions, Miscellany, and Prejudices | 315 |
Author Index | 349 | |
Subject Index | 353 |
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Add Techniques and Applications of Path Integration, Suitable for advanced undergraduates and graduate students, this text requires only a first course in quantum mechanics. The first part develops the techniques of path integration; the second section, dealing with applications, covers a host of illustrati, Techniques and Applications of Path Integration to the inventory that you are selling on WonderClubX
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Add Techniques and Applications of Path Integration, Suitable for advanced undergraduates and graduate students, this text requires only a first course in quantum mechanics. The first part develops the techniques of path integration; the second section, dealing with applications, covers a host of illustrati, Techniques and Applications of Path Integration to your collection on WonderClub |