• Cover (1)
• CONSTRUCTING QUANTUM MECHANICS (2)
• Copyright (5)
• Preface (6)
• Contents (12)
• List of plates (16)
• Chapter 1 Introduction to Volume One (26)
  • 1.1 Overview (26)
  • 1.2 Early developments: Planck, Einstein, and Bohr (27)
    • 1.2.1 Planck, the second law, and black-body radiation (27)
    • 1.2.2 Planck’s first tenuous steps toward energy quantization (29)
    • 1.2.3 Einstein, equipartition, and light quanta (29)
    • 1.2.4 Einstein, fluctuations, and light quanta (31)
    • 1.2.5 Lorentz convinces Planck of energy quantization (32)
    • 1.2.6 From Einstein, equipartition, and specific heat to Nernst and the Solvay conference (33)
    • 1.2.7 Bohr and Rutherford’s model of the atom (35)
    • 1.2.8 Bohr and Nicholson’s theory (37)
    • 1.2.9 The Balmer formula and the birth of the Bohr model of the atom (38)
    • 1.2.10 Einstein and the Bohr model (41)
  • 1.3 The old quantum theory: principles, successes, and failures (42)
    • 1.3.1 Sommerfeld’s path to quantum theory (43)
    • 1.3.2 Quantum conditions: Planck, Sommerfeld, Ishiwara, Wilson, Schwarzschild, and Epstein (47)
    • 1.3.3 Ehrenfest and the adiabatic principle (50)
    • 1.3.4 The correspondence principle from Bohr to Kramers, Born, and Van Vleck (54)
    • 1.3.5 The old quantum theory’s winning streak: fine structure, Stark effect, X-ray spectra (56)
    • 1.3.6 The old quantum theory’s luck runs out:multiplets, Zeeman effect, helium (60)
    • 1.3.7 Born taking stock (66)
• Part I Early Developments (68)
  • Chapter 2 Planck, the Second Law of Thermodynamics, and Black-body Radiation (70)
    • 2.1 The birthdate of quantum theory? (70)
    • 2.2 Early work on black-body radiation (1860–1896) (76)
    • 2.3 Planck, the second law of thermodynamics, and black-body radiation (1895–1899) (80)
    • 2.4 From the Wien law to the Planck law: changing the expression for the entropy of a resonator (90)
    • 2.5 Justifying the new expression for the entropy of a resonator (96)
    • 2.6 Energy parcels or energy bins? (102)
  • Chapter 3 Einstein, Equipartition, Fluctuations, and Quanta (109)
    • 3.1 Einstein’s annus mirabilis (109)
    • 3.2 The statistical trilogy (1902–1904) (111)
    • 3.3 The light-quantum paper (1905) (119)
      • 3.3.1 Classical theory leads to the Rayleigh–Jeans law (119)
      • 3.3.2 Einstein’s argument for light quanta: fluctuations in black-body radiation at high frequencies (121)
      • 3.3.3 Evidence for light quanta: the photoelectric effect (128)
    • 3.4 Black-body radiation and the necessity of quantization (132)
      • 3.4.1 The quantization of Planck’s resonators (132)
      • 3.4.2 Lorentz’s 1908 Rome lecture: Planck versus Rayleigh–Jeans (137)
      • 3.4.3 Einstein’s 1909 Salzburg lecture: fluctuations and wave–particle duality (142)
    • 3.5 The breakdown of equipartition and the specific heat of solids at low temperatures (1907–1911) (152)
    • 3.6 Einstein’s quantum theory of radiation (1916) (158)
      • 3.6.1 New derivation of the Planck law (159)
      • 3.6.2 Momentum fluctuations and the directed nature of radiation (163)
  • Chapter 4 The Birth of the Bohr Model (168)
    • 4.1 Introduction (168)
    • 4.2 The dissertation: recognition of problems of classical theory (170)
    • 4.3 The Rutherford Memorandum: atomic models and quantum theory (173)
      • 4.3.1 Prelude: classical atomic models (Thomson, Nagaoka, Schott) (174)
      • 4.3.2 Scattering of α particles and Rutherford’s nuclear atom (177)
      • 4.3.3 Bohr’s first encounter with Rutherford’s nuclear atom: energy loss of α particles traveling through matter (180)
      • 4.3.4 Interlude: Planck’s constant enters atomic modeling (Haas, Nicholson) (182)
      • 4.3.5 Planck’s constant enters Bohr’s atomic modeling (190)
    • 4.4 From the Rutherford Memorandum to the Trilogy (196)
      • 4.4.1 Bohr comparing his results to Nicholson’s (196)
      • 4.4.2 Enter the Balmer formula (200)
    • 4.5 The Trilogy: quantum atomic models and spectra (203)
      • 4.5.1 Part One: the hydrogen atom (204)
      • 4.5.2 Parts Two and Three: multi-electron atoms and multi-atom molecules (210)
    • 4.6 Early evidence for the Bohr model: spectral lines in hydrogen and helium (221)
• Part II The Old Quantum Theory (228)
  • Chapter 5 Guiding Principles (230)
    • 5.1 Quantization conditions (231)
      • 5.1.1 Planck (231)
      • 5.1.2 Wilson and Ishiwara (240)
      • 5.1.3 Sommerfeld (244)
      • 5.1.4 Schwarzschild, Epstein, and (once again) Sommerfeld (248)
      • 5.1.5 Einstein (253)
    • 5.2 The adiabatic principle (254)
      • 5.2.1 Ehrenfest’s early work on adiabatic invariants (255)
      • 5.2.2 Ehrenfest’s 1916 paper on the adiabatic principle (264)
      • 5.2.3 The adiabatic principle in Bohr’s 1918 paper (270)
      • 5.2.4 Sommerfeld’s attitude to the adiabatic principle (273)
    • 5.3 The correspondence principle (274)
  • Chapter 6 Successes (284)
    • 6.1 Fine structure (285)
    • 6.2 X-ray spectra (300)
    • 6.3 The Stark effect (309)
  • Chapter 7 Failures (325)
    • 7.1 The complex structure of spectral multiplets (326)
      • 7.1.1 Sommerfeld on multiplets (327)
      • 7.1.2 Heisenberg’s core model and multiplets (338)
    • 7.2 The anomalous Zeeman effect (343)
      • 7.2.1 The Lorentz theory of the normal Zeeman effect (344)
      • 7.2.2 Anomalous Zeeman effect: experimental results and pre-Bohr theoretical interpretations (346)
      • 7.2.3 The Paschen–Back transmutation of Zeeman lines (354)
    • 7.3 The Zeeman effect in the old quantum theory (358)
      • 7.3.1 First steps (1913–1919) (358)
      • 7.3.2 Empirical regularities and number mysticism (1919–1921) (362)
      • 7.3.3 Core models, unmechanical forces, and double-valuedness (371)
    • 7.4 The problem of helium (386)
  • Appendices (408)
  • A Classical Mechanics (410)
    • A.1 The physicist’s mechanical toolbox (ca 1915) (412)
      • A.1.1 Newtonian mechanics (412)
      • A.1.2 Lagrangian mechanics (414)
      • A.1.3 Hamiltonian mechanics (418)
      • A.1.4 The adiabatic principle (427)
    • A.2 The astronomer’s mechanical toolbox (ca 1915) (433)
      • A.2.1 Hamilton–Jacobi theory (433)
      • A.2.2 Poisson brackets (440)
      • A.2.3 Action-angle variables (443)
      • A.2.4 Canonical perturbation theory (448)
  • B Spectroscopy (455)
    • B.1 Early quantitative spectroscopy (455)
    • B.2 Kirchhoff’s Laws (458)
    • B.3 Technological advances and the emergence of analytic spectroscopy (459)
    • B.4 The numerology of spectra: Balmer and Rydberg (460)
    • B.5 The Zeeman effect (466)
    • B.6 A troublesome red herring (467)
    • B.7 Ritz and the combination principle (468)
  • Bibliography (474)
  • Index (506)