章节目录
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
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. Later chapters explore more advanced topics, including the perturbation method, quantum electrodynamics, and statistical mechanics. 1965 edition, with 2005 emendations.
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