Constructing quantum mechanics. Volume 2, The arch, 1923-1927 / Anthony Duncan and Michel Janssen.

Format:

Book

Author/Creator:

Duncan, Anthony (Professor of physics), author.

Janssen, Michel, 1960- author.

Series:

Oxford scholarship online.

Oxford scholarship online

Language:

English

Subjects (All):

Quantum theory--History--20th century.

Quantum theory.

Physical Description:

1 online resource (817 pages)

Other Title:

Arch, 1923-1927

Place of Publication:

Oxford : Oxford University Press, 2023.

Summary:

This is the second of two volumes on the genesis of quantum mechanics in the first quarter of the 20th century. It covers the rapid transition from the old to the new quantum theory in the years 1923-1927.

Contents:

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.

Notes:

Also issued in print: 2023.

Includes bibliographical references and index.

Description based on online resource and publisher information; title from PDF title page (viewed on September 13, 2023).

Other Format:

Print version: Janssen, Michel Constructing Quantum Mechanics Volume 2

ISBN:

0-19-199196-1

0-19-888391-9

OCLC:

1396988253