Constructing Quantum Mechanics Volume Two The Arch, 1923-1927

Michel Janssen, Professor for History of Science, School of Physics and Astronomy, Unversity of Minnesota,Antony 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.

8 Introduction to Volume 2
8.1. Overview
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 1925DS1927
15.2. Intermezzo: Kuhn losses suffered and recovered
15.3. External Field Problems 1925DS1927
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
Appendices
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