Quantum Mechanics and Path Integrals: Emended Edition

by Richard P. Feynman, Albert R. Hibbs, Daniel F. Styer

Overview

From astrophysics to condensed matter theory, nearly all of modern physics employs the path integral technique. In this presentation, the developer of path integrals and one of the best-known scientists of all time, Nobel Prize–winning physicist Richard P. Feynman, presents unique insights into this method and its applications. Avoiding dense, complicated descriptions, Feynman articulates his celebrated theory in a clear, concise manner, maintaining a perfect balance between mathematics and physics.
This emended edition of the original 1965 publication corrects hundreds of typographical errors and recasts many equations for clearer comprehension. It retains the original's verve and spirit, and it is approved and endorsed by the Feynman family. The opening chapters explore the fundamental concepts of quantum mechanics and introduce path integrals. Subsequent chapters cover more advanced topics, including the perturbation method, quantum electrodynamics, and the relation of path integrals to statistical mechanics. In addition to its merit as a text for graduate courses in physics, this volume serves as an excellent resource for professionals.

Product Details

ISBN-13:	9780486477220
Publisher:	Dover Publications
Publication date:	07/21/2010
Series:	Dover Books on Physics
Edition description:	Emended Editon
Pages:	384
Sales rank:	488,262
Product dimensions:	9.30(w) x 6.24(h) x 0.75(d)

About the Author

Richard Feynman (1918-88) received the 1965 Nobel Prize in Physics for his contributions to the development of quantum electrodynamics. One of the best-known scientists of his generation, Feynman assisted in the development of the atomic bomb and was a prominent member of the panel that investigated the 1986 Challenger disaster.
Known worldwide as the voice of NASA's Jet Propulsion Lab, Albert R. Hibbs (1924-2003) studied for his doctorate under Feynman's tutelage and transcribed and edited Feynman's lectures in quantum electrodynamics.
Daniel F. Styer holds a Ph.D. from Cornell University and is the John and Marianne Schiffer Professor of Physics at Oberlin College.

Richard P. Feynman: The Scientist's Scientist
One of the most famous scientists of the twentieth century, and an inexhaustible source of wonderful quotes, Richard Feynman shared the 1965 Nobel Prize in Physics with Julian Schwinger and Sin-Itiro Tomonaga for his contributions to the development of quantum electrodynamics. 1965 was also the year in which Feynman and A. R. Hibbs first published Quantum Mechanics and Path Integrals, which Dover reprinted in a new edition comprehensively emended by Daniel F. Styer in 2010.

In the Author's Own Words:
"Our freedom to doubt was born out of a struggle against authority in the early days of science. It was a very deep and strong struggle. It is our responsibility as scientists to proclaim the value of this freedom; to teach how doubt is not to be feared but welcomed and discussed; and to demand this freedom as our duty to all coming generations."

"I think I can safely say that nobody understands quantum mechanics."

"Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there."

"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. . . . If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." — Richard P. Feynman

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