图书简介

8 Introduction to Volume 2; 8.1 Overview; 8.2 Quantum theory in the early 1920s: deficiencies and discoveries; 8.3 Atomic structure a 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 [Dreimannerarbeit]-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 Schrodinger’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.Schrodinger and Wave Mechanics; 14.1 Erwin Schrodinger: early work in quantum theory; 14.2 Schrodinger 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; 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

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