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Constructing Quantum Mechanics Volume 2

The Arch, 1923-1927

Prof Michel Janssen and Prof Anthony Duncan

20 July 2023

ISBN: 9780198883906

752 pages

Price: £85.00

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.



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.

  • Careful selection of the most important strands in the development of quantum mechanics
  • Detailed analysis of all classic papers leading up to and establishing modern quantum mechanics
  • Appendix on the mathematics of the new quantum theory
  • Detailed bibliography of both primary and secondary sources as well as a detailed person and subject index
  • Set of “web resources” (made available on the web page for the book) providing further details on derivations covered in the main text

About the Author(s)

Prof Michel Janssen, Professor for History of Science, School of Physics and Astronomy, Unversity of Minnesota, and Prof Anthony Duncan, Professor of Physics Emeritus, University of Pittsburgh

Michel Janssen studied physics and philosophy at the University of Amsterdam and history and philosophy of science at the University of Pittsburgh, where he earned his PhD in 1995. He was an editor at the Einstein Papers Project before joining the School of Physics and Astronomy at the University of Minnesota as a historian of science in 2000. He has also been a regular visitor at the Max Planck Institute for History of Science in Berlin. His research focuses on the genesis of relativity and quantum theory.

Anthony Duncan received his PhD in theoretical elementary particle physics in 1975 from the Massachusetts Institute of Technology, under the supervision of Steven Weinberg. Following postdoctoral and junior faculty positions at the Institute for Advanced Study in Princeton and Columbia University in New York, he joined the faculty of the Department of Physics and Astronomy at the University of Pittsburgh in 1981 as Associate Professor of Physics. He has taught a wide range of courses, both at the undergraduate and graduate level, including courses on the history of modern physics. He is now (since 2015) Professor Emeritus of Physics at the University of Pittsburgh.

Table of Contents

    8 Introduction to Volume 2
    8.2:Quantum theory in the early 1920s: deficiencies and discoveries
    8.3:Atomic structure à la Bohr
    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—the Two-Man-Paper of Born and Jordan
    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. Erwin 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
    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 of 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
    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
    12.1:The “Two-Man-Paper” of Born and Jordan
    12.2: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:Erwin 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
    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
    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: the von Neumann spectral theory


"Review from previous edition An excellent work which innovatively combines conceptual clarity with penetrating analysis of relevant theory." - Helge Kragh, Annals of Science

"Engineers and scientists from across the board will get a kick out of being able to read about the origins of their everyday toolkits - this is lucid historical reasoning about one of the great accomplishments of modern science. After seeing the author's track the launch of the old quantum theory, I'm looking forward to their account of full-blown quantum mechanics to come in volume 2!" - Peter Galison, Harvard University

"Clearly written, by highly competent authors, giving full reasoning and calculations for all important developments." - Olivier Darrigol, CNRS, France

"This will be a widely read book and used in many physics and history of physics courses at the undergraduate college-university level. It will be greeted most enthusiastically by scholars and teachers alike." - Roger H. Stuewer, University of Minnesota

"Indeed a very important and valuable contribution to the history of quantum mechanics." - Michael Eckert, Deutsches Museum, Muenchen

"What seemed a good piece of work at the start is magisterial. This is the book I have been waiting to see for a long time." - Steven N. Shore, University of Pisa

"This book will very likely become a new point of reference for everyone working on the history of quantum physics." - Christian Joas, Niels Bohr Archive