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

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The history of quantum theory is a maze of conceptual problems, through which Olivier Darrigol provides a lucid and learned guide, tracking the role of formal analogies between classical and quantum theory. From Planck's first introduction of the quantum of action to Dirac's formulation of quantum mechanics, Darrigol illuminates not only the history of quantum theory but also the role of analogies in scientific thinking and theory change.

Unlike previous works, which have tended...

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Overview

The history of quantum theory is a maze of conceptual problems, through which Olivier Darrigol provides a lucid and learned guide, tracking the role of formal analogies between classical and quantum theory. From Planck's first introduction of the quantum of action to Dirac's formulation of quantum mechanics, Darrigol illuminates not only the history of quantum theory but also the role of analogies in scientific thinking and theory change.

Unlike previous works, which have tended to focus on qualitative, global arguments, Darrigol's study follows the lines of mathematical reasoning and symbolizing and so is able to show the motivations of early quantum theorists more precisely—and provocatively—than ever before. Erudite and original, From c-Numbers to q-Numbers sets a new standard as a philosophically perceptive and mathematically precise history of quantum mechanics. For years to come it will influence historical and philosophical discussions of twentieth-century physics.

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Darrigol tracks the role of formal analogies between classical and quantum theory--from Planck's first introduction of the quantum of action to Dirac's formulation of quantum mechanics--illuminating not only the history of quantum theory but also the role of analogies in scientific thinking and theory change. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Meet the Author

A physicist and historian of physics, Olivier Darrigol is a chargé de recherches at the Centre National de la Recherche Scientifique in Paris and a lecturer in history of physics at the Ecole Normale Supérieure.

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Table of Contents

Acknowledgments
Conventions and Notations
Introduction
Pt. A Planck's Radiation Theory 1
Introduction 3
1 Concepts of Gas Theory 7
Maxwell's Collision Formula 7
Boltzmann's Irreversible Equations 13
The Nature of Irreversibility 15
2 Planck's Absolute Irreversibility 22
Against Atoms 22
Blackbody Radiation 24
Planck's Resonators 29
3 On Irreversible Radiation Processes 39
A Polemic with Boltzmann 39
Natural Radiation 41
Planck Versus Boltzmann 51
4 The Infrared Challenge 57
The Second Derivative of the Resonator Entropy 57
Boltzmann's Combinatorics 62
Quantified Chaos 66
Quantum Continuity 70
Pt. B The Correspondence Principle 79
Introduction 81
5 The Bohr Atom (1913-1916) 85
Horrid Assumptions 85
Confirmations and Perturbations 89
Periodic Systems 93
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 or Reason? 137
7 Harmonic Interplay 150
Beyond Multiperiodic Systems 150
Building Atoms 154
Systematic Calculations 168
8 A Crisis 175
The Catastrophe of Helium 175
Orbit-Killers in the Zeeman Jungle 179
The Exclusion Principle 201
9 The Virtual Orchestra 213
The Theory of Bohr, Kramers, and Slater (BKS) 214
Dispersion Theory 224
Intensities 235
The Fall of the BKS Theory 246
10 Matrix Mechanics 260
From Copenhagen to Gottingen 260
Umdeutung 263
Guiding Principles 273
Epilogue 276
Pt. C Dirac's Quantum Mechanics 285
Introduction 287
11 Classical Beauty 291
Noncommutative Geometry 291
The Lesson of Relativity 297
The Art of Action-Angle Variables 304
12 Queer Numbers 309
Poisson Resurrected 309
The Canonical Method 317
Quantum Algebra 319
13 Quantum Beauty 329
Schrodinger's Equation 329
Transformations 333
Welcome to Copenhagen 343
Bibliographical Guide 349
Abbreviations Used in Citations and in the Bibliography 354
Bibliography of Secondary Literature 356
Bibliography of Primary Literature 368
Index 381
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