From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory

801 Pages·1993·4.69 MB·English

by  Olivier Darrigol

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Page ii
From c-Numbers to q-Numbers
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CALIFORNIA STUDIES IN THE HISTORY OF SCIENCE
J. L. HEILBRON, Editor
The Galileo Affair: A Documentary History, edited and translated by
Maurice A. Finocchiaro
The New World, 1939-1946 (A History of the United States Atomic
Energy Commission, volume 1), by Richard G. Hewlett and Oscar E.
Anderson, Jr.
Atomic Shield, 1947-1952 (A History of the United States Atomic
Energy Commission, volume 2), by Richard G. Hewlett and Francis
Duncan
Atoms for Peace and War, 1953-1961: Eisenhower and the Atomic
Energy Commission (A History of the United States Atomic Energy
Commission, volume 3), by Richard G. Hewlett and Jack M. Holl
Lawrence and His Laboratory: A History of the Lawrence Berkeley
Laboratory, Volume 1, by J. L. Heilbron and Robert W. Seidel
Scientific Growth: Essays on the Social Organization and Ethos of
Science, by Joseph Ben-David, edited by Gad Freudenthal
Physics and Politics in Revolutionary Russia, by Paul R. Josephson
From c-Numbers to q-Numbers: The Classical Analogy in the History
of Quantum Theory, by Olivier Darrigol
Page iv
From c-Numbers To q-Numbers
The Classical Analogy in the History of Quantum Theory
Olivier Darrigol
UNIVERSITY OF CALIFORNIA PRESS
Berkeley · Los Angeles ·Oxford
Page v
University of California Press
Berkeley and Los Angeles, California
University of California Press
Oxford, England
Copyright © 1992 by The Regents of the University of California
Library of Congress Cataloging-in-Publication Data
Darrigol, Olivier.
From c-numbers to q-numbers: the classical analogy in the history
of quantum theory / Olivier Darrigol.
p. cm. (California studies in the history of science)
Includes bibliographical references and index.
ISBN 0-520-07822-5
1. Quantum theoryHistory. I. Title. II. Series.
QC173.98.D37 1992
530.1'2'09dc20 91-42469
CIP
Printed in the United States of America
1 2 3 4 5 6 7 8 9
The paper used in this publication meets the minimum requirements
of American National Standard for Information SciencesPermanence
of Paper for Printed Library Materials, ANSI Z39.48-1984
Page vi
A mes Parents
Page vii
CONTENTS
Acknowledgments xi
Conventions and Notations xiii
Introduction xv
Part A. Planck's Radiation Theory
Introduction
1. Concepts of Gas Theory 7
Maxwell's Collision Formula 7
Boltzmann's Irreversible Equations 13
The Nature of Irreversibility 15
Summary 19
2. Planck's Absolute Irreversibility 22
Against Atoms 22
Blackbody Radiation 24
Planck's Resonators 29
Summary 36
3. On Irreversible Radiation Processes 39
A Polemic with Boltzmann 39
Natural Radiation 41
Page viii
Planck Versus Boltzmann 51
Summary 54
4. The Infrared Challenge 57
The Second Derivative of the Resonator Entropy 57
Boltzmann's Combinatorics 62
Quantified Chaos 66
Quantum Continuity 70
Summary and Conclusions 73
Part B. The Correspondence Principle 79
Introduction 81
5. The Bohr Atom (1913-1916) 85
Horrid Assumptions 85
Confirmations and Perturbations 89
Periodic Systems 93
Summary 98
6. Postulates and Principles 102
Multiperiodic Systems 102
Einstein's Transition Probabilities 118
"On the Quantum Theory of Line Spectra" 121
The Meaning of the Correspondence Principle: Magic 137
or Reason?
Summary 145
7. Harmonic Interplay 150
Beyond Multiperiodic Systems 150
Building Atoms 154
Systematic Calculations 168
Summary 171
8. A Crisis 175
The Catastrophe of Helium 175
Orbit-Killers in the Zeeman Jungle 179
The Exclusion Principle 201
Summary 209
9. The Virtual Orchestra 213
The Theory of Bohr, Kramers, and Slater (BKS) 214
Dispersion Theory 224
Intensities 235
Page ix
The Fall of the BKS Theory 246
Summary 255
10. Matrix Mechanics 260
From Copenhagen to Göttingen 260
Umdeutung 263
Guiding Principles 273
Epilogue 276
Summary and Conclusions 280
Part C. Dirac's Quantam Mechanics 285
Introduction 287
11. Classical Beauty 291
Noncommutative Geometry 291
The Lesson of Relativity 297
The Art of Action-Angle Variables 304
Summary 306
12. Queer Numbers 309
Poisson Resurrected 309
The Canonical Method 317
Quantum Algebra 319
Summary 325
13. Quantum Beauty 329