Quantum Mechanics and Path Integrals Emended Edition

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

• ISBN13: 9780486477220
• ISBN10: 0486477223
• Format: Paperback
• Copyright: 2010-07-21
• Publisher: Dover Publications
• More Book Details
• Purchase Benefits

Summary

The developer of path integrals, Nobel Prizewinning 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.

Author Biography

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