Keywords:
Quantum theory.
;
Electronic books.
Description / Table of Contents:
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.
Type of Medium:
Online Resource
Pages:
1 online resource (817 pages)
Edition:
1st ed.
ISBN:
9780198883913
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=7282240
DDC:
530.1209
Language:
English
Note:
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.
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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.
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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.
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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.
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