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Quantum Mechanics and Path Integrals：Emended Edition

Quantum Mechanics and Path Integrals：Emended Edition

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作者: Richard P. Feynman , Albert R. Hibbs , Daniel F. Styer

出版社: Dover Publications

出版时间: 2010-07

ISBN: 9780486477220

装帧: 其他

开本: 其他

纸张: 其他

分类: 外文古旧书>英文书>文学

7人买过

The developer of path integrals, Nobel Prize-winning physicist Richard Feynman presents unique insights into this method and its applications. Feynman starts with an intuitive view of fundamental quantum mechanics, gradually introducing path integrals. La Table of Contents
Preface v
Preface to Emended Edition viii
Chapter 1 The Fundamental Concepts of Quantum Mechanics 1
1-1 Probability in quantum mechanics 2
1-2 The uncertainty principle 9
1-3 Interfering alternatives 13
1-4 Summary of probability concepts 19
1-5 Some remaining thoughts 22
1-6 The purpose of this book 23
Chapter 2 The Quantum-mechanical Law of Motion 25
2-1 The classical action 26
2-2 The quantum-mechanical amplitude 28
2-3 The classical limit 29
2-4 The sum over paths 31
2-5 Events occurring in succession 36
2-6 Some remarks 39
Chapter 3 Developing the Concepts with Special Examples 41
3-1 The free particle 42
3-2 Diffraction through a slit 47
3-3 Results for a sharp-edged slit 55
3-4 The wave function 57
3-5 Gaussian integrals 58
3-6 Motion in a potential field 62
3-7 Systems with many variables 65
3-8 Separable systems 66
3-9 The path integral as a functional 68
3-10 Interaction of a particle and a harmonic oscillator 69
3-11 Evaluation of path integrals by Fourier series 71
Chapter 4 The Schrödinger Description of Quantum Mechanics 75
4-1 The Schrödinger equation 76
4-2 The time-independent hamiltonian 84
4-3 Normalizing the free-particle wave functions 89
Chapter 5 Measurements and Operators 95
5-1 The momentum representation 96
5-2 Measurement of quantum-mechanical variables 106
5-3 Operators 112
Chapter 6 The Perturbation Method in Quantum Mechanics 119
6-1 The perturbation expansion 120
6-2 An integral equation for KV 126
6-3 An expansion for the wave function 127
6-4 The scattering of an electron by an atom 129
6-5 Time-dependent perturbations and transition amplitudes 144
Chapter 7 Transition Elements 163
7-1 Definition of the transition element 164
7-2 Functional derivatives 170
7-3 Transition elements of some special functionals 174
7-4 General results for quadratic actions 182
7-5 Transition elements and the operator notation 184
7-6 The perturbation series for a vector potential 189
7-7 The hamiltonian 192
Chapter 8 Harmonic Oscillators 197
8-1 The simple harmonic oscillator 198
8-2 The polyatomic molecule 203
8-3 Normal coordinates 208
8-4 The one-dimensional crystal 212
8-5 The approximation of continuity 218
8-6 Quantum mechanics of a line of atoms 222
8-7 The three-dimensional crystal 224
8-8 Quantum field theory 229
8-9 The forced harmonic oscillator 232
Chapter 9 Quantum Electrodynamics 235
9-1 Classical electrodynamics 237
9-2 The quantum mechanics of the rediation field 242
9-3 The ground state 244
9-4 Interaction of field and matter 247
9-5 A single electron in a radiative field 253
9-6 The Lamb shift 256
9-7 The emission of light 260
9-8 Summary 262
Chapter 10 Statistical Mechanics 267
10-1 The partition function 269
10-2 The path integral evaluation 273
10-3 Quantum-mechanical effects 279
10-4 Systems of several variables 287
10-5 Remarks on methods of derivation 296
Chapter 11 The Variational Method 299
11-1 A minimum principle 300
11-2 An application of the variational method 303
11-3 The standard variational principle 307
11-4 Slow electrons in a polar crystal 310
Chapter 12 Other Problems in Probability 321
12-1 Random pulses 322
12-2 Characteristic functions 324
12-3 Noise 327
12-4 Gaussian noise 332
12-5 Noise spectrum 334
12-6 Brownian motion 337
12-7 Quantum mechanics 341
12-8 Influence functionals 344
12-9 Influence functional from a harmonic oscillator 352
12-10 Conclusions 356
Appendix: Some Useful Definite Integrals 359
Appendix: Notes 361
Index 366
内容简介:
The developer of path integrals, Nobel Prize-winning physicist Richard Feynman presents unique insights into this method and its applications. Feynman starts with an intuitive view of fundamental quantum mechanics, gradually introducing path integrals. La
目录:
Table of Contents
Preface v
Preface to Emended Edition viii
Chapter 1 The Fundamental Concepts of Quantum Mechanics 1
1-1 Probability in quantum mechanics 2
1-2 The uncertainty principle 9
1-3 Interfering alternatives 13
1-4 Summary of probability concepts 19
1-5 Some remaining thoughts 22
1-6 The purpose of this book 23
Chapter 2 The Quantum-mechanical Law of Motion 25
2-1 The classical action 26
2-2 The quantum-mechanical amplitude 28
2-3 The classical limit 29
2-4 The sum over paths 31
2-5 Events occurring in succession 36
2-6 Some remarks 39
Chapter 3 Developing the Concepts with Special Examples 41
3-1 The free particle 42
3-2 Diffraction through a slit 47
3-3 Results for a sharp-edged slit 55
3-4 The wave function 57
3-5 Gaussian integrals 58
3-6 Motion in a potential field 62
3-7 Systems with many variables 65
3-8 Separable systems 66
3-9 The path integral as a functional 68
3-10 Interaction of a particle and a harmonic oscillator 69
3-11 Evaluation of path integrals by Fourier series 71
Chapter 4 The Schrödinger Description of Quantum Mechanics 75
4-1 The Schrödinger equation 76
4-2 The time-independent hamiltonian 84
4-3 Normalizing the free-particle wave functions 89
Chapter 5 Measurements and Operators 95
5-1 The momentum representation 96
5-2 Measurement of quantum-mechanical variables 106
5-3 Operators 112
Chapter 6 The Perturbation Method in Quantum Mechanics 119
6-1 The perturbation expansion 120
6-2 An integral equation for KV 126
6-3 An expansion for the wave function 127
6-4 The scattering of an electron by an atom 129
6-5 Time-dependent perturbations and transition amplitudes 144
Chapter 7 Transition Elements 163
7-1 Definition of the transition element 164
7-2 Functional derivatives 170
7-3 Transition elements of some special functionals 174
7-4 General results for quadratic actions 182
7-5 Transition elements and the operator notation 184
7-6 The perturbation series for a vector potential 189
7-7 The hamiltonian 192
Chapter 8 Harmonic Oscillators 197
8-1 The simple harmonic oscillator 198
8-2 The polyatomic molecule 203
8-3 Normal coordinates 208
8-4 The one-dimensional crystal 212
8-5 The approximation of continuity 218
8-6 Quantum mechanics of a line of atoms 222
8-7 The three-dimensional crystal 224
8-8 Quantum field theory 229
8-9 The forced harmonic oscillator 232
Chapter 9 Quantum Electrodynamics 235
9-1 Classical electrodynamics 237
9-2 The quantum mechanics of the rediation field 242
9-3 The ground state 244
9-4 Interaction of field and matter 247
9-5 A single electron in a radiative field 253
9-6 The Lamb shift 256
9-7 The emission of light 260
9-8 Summary 262
Chapter 10 Statistical Mechanics 267
10-1 The partition function 269
10-2 The path integral evaluation 273
10-3 Quantum-mechanical effects 279
10-4 Systems of several variables 287
10-5 Remarks on methods of derivation 296
Chapter 11 The Variational Method 299
11-1 A minimum principle 300
11-2 An application of the variational method 303
11-3 The standard variational principle 307
11-4 Slow electrons in a polar crystal 310
Chapter 12 Other Problems in Probability 321
12-1 Random pulses 322
12-2 Characteristic functions 324
12-3 Noise 327
12-4 Gaussian noise 332
12-5 Noise spectrum 334
12-6 Brownian motion 337
12-7 Quantum mechanics 341
12-8 Influence functionals 344
12-9 Influence functional from a harmonic oscillator 352
12-10 Conclusions 356
Appendix: Some Useful Definite Integrals 359
Appendix: Notes 361
Index 366

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