This is the second of two volumes on the genesis of quantum mechanics in the first quarter of the 20th century. It covers the period 1923-1927. After covering some of the difficulties the old quantum theory had run into by the early 1920s as well as the discovery of the exclusion principle and electron spin, it traces the emergence of two forms of the new quantum mechanics, matrix mechanics and wave mechanics, in the years 1923-27. It then shows how the new theory took care of some of the failures of the old theory and put its successes on a more solid basis. Finally, it shows how in 1927 the two forms of the new theory were unified, first through statistical transformation theory, then through the Hilbert space formalism.
This volume provides a detailed analysis of the classic papers by Heisenberg, Born, Jordan, Dirac, De Broglie, Einstein, Schrödinger, von Neumann and other authors. Drawing on the correspondence of these and other physicists, their later reminiscences and the extensive secondary literature on the “quantum revolution”, this volume places these papers in the context of the discussions out of which modern quantum mechanics emerged. It argues that the genesis of modern quantum mechanics can be seen as the construction of an arch on a scaffold provided by the old quantum theory, discarded once the arch could support itself.
Author(s): Anthony Duncan; Michel Janssen;
Edition: 1
Publisher: Oxford University Press
Year: 2023
Language: English
Pages: xv; 794
City: New York
Tags: Science & Mathematics > Physics; Science & Mathematics > Physics > Quantum Physics
Cover
Titlepage
Copyright
Dedication
Preface
Contents
List of Plates
8 Introduction to Volume 2
8.1 Overview
8.2 Quantum theory in the early 1920s: deficiencies and discoveries (exclusion principle and spin)
8.3 Atomic structure à la Bohr, X-ray spectra, and the discovery of the exclusion principle
8.3.1 Important clues from X-ray spectroscopy
8.3.2 Electron arrangements and the emergence of the exclusion principle
8.3.3 The discovery of electron spin
8.4 The dispersion of light: a gateway to a new mechanics
8.4.1 The Lorentz–Drude theory of dispersion
8.4.2 Dispersion theory and the Bohr model
8.4.3 Final steps to a correct quantum dispersion formula
8.4.4 A generalized dispersion formula for inelastic light scattering—the Kramers–Heisenberg paper
8.5 The genesis of matrix mechanics
8.5.1 Intensities, and another look at the hydrogen atom
8.5.2 The Umdeutung paper
8.5.3 The new mechanics receives an algebraic framing—Born and Jordan's Two-Man-Paper
8.5.4 Dirac and the formal connection between classical and quantum mechanics
8.5.5 The Three-Man-Paper [Dreimännerarbeit]—completion of the formalism of matrix mechanics
8.6 The genesis of wave mechanics
8.6.1 The mechanical-optical route to quantum mechanics
8.6.2 Schrödinger's wave mechanics
8.7 The new theory repairs and extends the old
8.8 Statistical aspects of the new quantum formalisms
8.9 The Como and Solvay conferences, 1927
8.10 Von Neumann puts quantum mechanics in Hilbert space
Part III Transition to the New Quantum Theory
9 The Exclusion Principle and Electron Spin
9.1 The road to the exclusion principle
9.1.1 Bohr's second atomic theory
9.1.2 Clues from X-ray spectra
9.1.3 The filling of electron shells and the emergence of the exclusion principle
9.2 The discovery of electron spin
10 Dispersion Theory in the Old Quantum Theory
10.1 Classical theories of dispersion
10.1.1 Damped oscillations of a charged particle
10.1.2 Forced oscillations of a charged particle
10.1.3 The transmission of light: dispersion and absorption
10.1.4 The Faraday effect
10.1.5 The empirical situation up to ca. 1920
10.2 Optical dispersion and the Bohr atom
10.2.1 The Sommerfeld–Debye theory
10.2.2 Dispersion theory in Breslau: Ladenburg and Reiche
10.3 The correspondence principle in radiation and dispersion theory: Van Vleck and Kramers
10.3.1 Van Vleck and the correspondence principle for emission and absorption of light
10.3.2 Dispersion in a classical general multiply periodic system
10.3.3 The Kramers dispersion formula
10.4 Intermezzo: the BKS theory and the Compton effect
10.5 The Kramers–Heisenberg paper and the Thomas–Reiche–Kuhn sum rule: on the verge of Umdeutung
11 Heisenberg's Umdeutung Paper
11.1 Heisenberg in Copenhagen
11.2 A return to the hydrogen atom
11.3 From Fourier components to transition amplitudes
11.4 A new quantization condition
11.5 Heisenberg's Umdeutung paper: a new kinematics
11.6 Heisenberg's Umdeutung paper: a new mechanics
12 The Consolidation of Matrix Mechanics: Born–Jordan, Dirac and the Three-Man-Paper
12.1 The ``Two-Man-Paper'' of Born and Jordan
12.2 The new theory derived differently: Dirac's formulation of quantum mechanics
12.3 The ``Three-Man-Paper'' of Born, Heisenberg, and Jordan
12.3.1 First chapter: systems of a single degree of freedom
12.3.2 Second chapter: foundations of the theory of systems of arbitrarily many degrees of freedom
12.3.3 Third chapter: connection with the theory of eigenvalues of Hermitian forms
12.3.4 Third chapter (cont'd): continuous spectra
12.3.5 Fourth chapter: physical applications of the theory
13 De Broglie's Matter Waves and Einstein's Quantum Theory of the Ideal Gas
13.1 De Broglie and the introduction of wave–particle duality
13.2 Wave interpretation of a particle in uniform motion
13.3 Classical extremal principles in optics and mechanics
13.4 De Broglie's mechanics of waves
13.5 Bose–Einstein statistics and Einstein's quantum theory of the ideal gas
14 Schrödinger and Wave Mechanics
14.1 Schrödinger: early work in quantum theory
14.2 Schrödinger and gas theory
14.3 The first (relativistic) wave equation
14.4 Four papers on non-relativistic wave mechanics
14.4.1 Quantization as an eigenvalue problem. Part I
14.4.2 Quantization as an eigenvalue problem. Part II
14.4.3 Quantization as an eigenvalue problem. Part III
14.4.4 Quantization as an eigenvalue problem. Part IV
14.5 The ``equivalence'' paper
14.6 Reception of wave mechanics
15 Successes and Failures of the Old Quantum Theory Revisited
15.1 Fine structure 1925–1927
15.2 Intermezzo: Kuhn losses suffered and recovered
15.3 External field problems 1925–1927
15.3.1 The anomalous Zeeman effect: matrix-mechanical treatment
15.3.2 The Stark effect: wave-mechanical treatment
15.4 The problem of helium
15.4.1 Heisenberg and the helium spectrum: degeneracy, resonance, and the exchange force
15.4.2 Perturbative attacks on the multi-electron problem
15.4.3 The helium ground state: perturbation theory gives way to variational methods
Part IV The Formalism of Quantum Mechanics and Its Statistical Interpretation
16 Statistical Interpretation of Matrix and Wave Mechanics
16.1 Evolution of probability concepts from the old to the new quantum theory
16.2 The statistical transformation theory of Jordan and Dirac
16.2.1 Jordan's and Dirac's versions of the statistical transformation theory
16.2.2 Jordan's ``New foundation …'' I
16.2.3 Hilbert, von Neumann, and Nordheim on Jordan's ``New foundation …'' I
16.2.4 Jordan's ``New foundation …'' II
16.3 Heisenberg's uncertainty relations
16.4 Como and Solvay, 1927
17 Von Neumann's Hilbert Space Formalism
17.1 ``Mathematical foundation …''
17.2 ``Probability-theoretic construction …''
17.3 From canonical transformations to transformations in Hilbert space
18 Conclusion: Arch and Scaffold
18.1 Continuity and discontinuity in the quantum revolution
18.2 Continuity and discontinuity in two early quantum textbooks
18.3 The inadequacy of Kuhn's model of a scientific revolution
18.4 Evolution of species and evolution of theories
18.5 The role of constraints in the quantum revolution
18.6 Limitations of the arch-and-scaffold metaphor
18.7 Substitution and generalization
Appendix
C C. The Mathematics of Quantum Mechanics
C.1 Matrix algebra
C.2 Vector spaces (finite dimensional)
C.3 Inner-product spaces (finite dimensional)
C.4 A historical digression: integral equations and quadratic forms
C.5 Infinite-dimensional spaces
C.5.1 Topology: open and closed sets, limits, continuous functions, compact sets
C.5.2 The first Hilbert space: l2
C.5.3 Function spaces: L2
C.5.4 The axiomatization of Hilbert space
C.5.5 A new notation: Dirac's bras and kets
C.5.6 Operators in Hilbert space: von Neumann's spectral theory
Bibliography
Index
