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Quantum Concepts in Physics

Book Description

Written for advanced undergraduates, physicists, and historians and philosophers of physics, this book tells the story of the development of our understanding of quantum phenomena through the extraordinary years of the first three decades of the twentieth century. Rather than following the standard axiomatic approach, this book adopts a historical perspective, explaining clearly and authoritatively how pioneers such as Heisenberg, Schrodinger, Pauli and Dirac developed the fundamentals of quantum mechanics and merged them into a coherent theory, and why the mathematical infrastructure of quantum mechanics has to be as complex as it is. The author creates a compelling narrative, providing a remarkable example of how physics and mathematics work in practice. The book encourages an enhanced appreciation of the interaction between mathematics, theory and experiment, helping the reader gain a deeper understanding of the development and content of quantum mechanics than any other text at this level.

Table of Contents

  1. Cover
  2. QuantumConcepts in Physics
  3. Title Page
  4. Copyright
  5. Dedication
  6. Table of Contents
  7. Preface
  8. Acknowledgements
  9. Part I The Discovery of Quanta
    1. Chapter 1 Physics and theoretical physics in 1895
      1. 1.1 The triumph of nineteenth century physics
      2. 1.2 Atoms and molecules in the nineteenth century
      3. 1.3 The kinetic theory of gases and Boltzmann’s statistical mechanics
      4. 1.4 Maxwell’s equations for the electromagnetic field
      5. 1.5 The Michelson–Morley experiment and the theory of relativity
      6. 1.6 The origin of spectral lines
      7. 1.7 The spectrum of black-body radiation
      8. 1.8 The gathering storm
    2. Chapter 2 Planck and black-body radiation
      1. 2.1 The key role of experimental technique
      2. 2.2 1895–1900: The changing landscape of experimental physics
      3. 2.3 Planck and the spectrum of black-body radiation
      4. 2.4 Towards the spectrum of black-body radiation
      5. 2.5 Comparison of the laws for black-body radiation with experiment
      6. 2.6 Planck’s theory of black-body radiation
      7. 2.7 Planck and ‘natural units’
      8. 2.8 Planck and the physical significance of h
    3. Chapter 3 Einstein and quanta 1900–1911
      1. 3.1 Einstein in 1905
      2. 3.2 Einstein on Brownian motion
      3. 3.3 On a heuristic viewpoint concerning the production and transformation of light (Einstein 1905a)
      4. 3.4 The quantum theory of solids
      5. 3.5 Debye’s theory of specific heats
      6. 3.6 Fluctuations of particles and waves – Einstein (1909)
      7. 3.7 The First Solvay Conference
      8. 3.8 The end of the beginning
  10. Part II The Old Quantum Theory
    1. Chapter 4 The Bohr model of the hydrogen atom 71
      1. 4.1 The Zeeman effect: Lorentz and Larmor’s interpretations
      2. 4.2 The problems of building models of atoms
      3. 4.3 Thomson and Rutherford
      4. 4.4 Haas’s and Nicholson’s models of atoms
      5. 4.5 The Bohr model of the hydrogen atom
      6. 4.6 Moseley and the X-ray spectra of the chemical elements
      7. 4.7 The Franck–Hertz experiment
      8. 4.8 The reception of Bohr’s theory of the atom
    2. Chapter 5 Sommerfeld and Ehrenfest – generalising the Bohr model
      1. 5.1 Introduction
      2. 5.2 Sommerfeld’s extension of the Bohr model to elliptical orbits
      3. 5.3 Sommerfeld and the fine-structure constant
      4. 5.4 A mathematical interlude – from Newton to Hamilton–Jacobi
      5. 5.5 Sommerfeld’s model of the atom in three dimensions
      6. 5.6 Ehrenfest and the adiabatic principle
      7. 5.7 The developing infrastructure of quantum theory
    3. Chapter 6 Einstein coefficients, Bohr’s correspondence principle and the first selection rules
      1. 6.1 The problem of transitions between stationary states
      2. 6.2 On the quantum theory of radiation (Einstein 1916)
      3. 6.3 Bohr’s correspondence principle
      4. 6.4 The first selection rules
      5. 6.5 The polarisation of quantised radiation and selection rules
      6. 6.6 The Rydberg series and the quantum defect
      7. 6.7 Towards a more complete quantum theory of atoms
    4. Chapter 7 Understanding atomic spectra – additional quantum numbers
      1. 7.1 Optical spectroscopy, multiplets and the splitting of spectral lines
      2. 7.2 The Stark effect
      3. 7.3 The Zeeman effect
      4. 7.4 The anomalous Zeeman effect
      5. 7.5 The Barnett, Einstein–de Haas and Stern–Gerlach experiments
    5. Chapter 8 Bohr’s model of the periodic table and the origin of spin
      1. 8.1 Bohr’s first model of the periodic table
      2. 8.2 The Wolfskehl lectures and Bohr’s second theory of the periodic table
      3. 8.3 X-ray levels and Stoner’s revised periodic table
      4. 8.4 Pauli’s exclusion principle
      5. 8.5 The spin of the electron
    6. Chapter 9 The wave–particle duality
      1. 9.1 The Compton effect
      2. 9.2 Bose–Einstein statistics
      3. 9.3 De Broglie waves
      4. 9.4 Electron diffraction
      5. 9.5 What had been achieved by the end of 1924
  11. Part III The Discovery of Quantummechanics
    1. Chapter 10 The collapse of the old quantum theory and the seeds of its regeneration 189
      1. 10.1 Ladenburg, Kramers and the theory of dispersion
      2. 10.2 Slater and the Bohr–Kramers–Slater theory
      3. 10.3 Born and ‘quantum mechanics’
      4. 10.4 Mathematics and physics in Göttingen
    2. Chapter 11 The Heisenberg breakthrough
      1. 11.1 Heisenberg in Göttingen, Copenhagen and Helgoland
      2. 11.2 Quantum-theoretical re-interpretation of kinematic and mechanical relations (Heisenberg, 1925)
      3. 11.3 The radiation problem and the translation from classical to quantum physics
      4. 11.4 The new dynamics
      5. 11.5 The nonlinear oscillator
      6. 11.6 The simple rotator
      7. 11.7 Reflections
    3. Chapter 12 Matrix mechanics
      1. 12.1 Born’s reaction
      2. 12.2 Born and Jordan’s matrix mechanics
      3. 12.3 Born, Heisenberg and Jordan (1926) – the Three-Man Paper
      4. 12.4 Pauli’s theory of the hydrogen atom
      5. 12.5 The triumph of matrix mechanics and its incompleteness
    4. Chapter 13 Dirac’s quantum mechanics
      1. 13.1 Dirac’s approach to quantum mechanics
      2. 13.2 Dirac and The fundamental equations of quantum mechanics (1925)
      3. 13.3 Quantum algebra, q- and c numbers and the hydrogen atom
      4. 13.4 Multi-electron atoms, On quantum algebra and a PhD dissertation
    5. Chapter 14 Schrödinger and wave mechanics
      1. 14.1 Schrödinger’s background in physics and mathematics
      2. 14.2 Einstein, De Broglie and Schrödinger
      3. 14.3 The relativistic Schrödinger wave equation
      4. 14.4 Quantisation as an Eigenvalue Problem (Part 1)
      5. 14.5 Quantisation as an eigenvalue problem (Part 2)
      6. 14.6 Wave-packets
      7. 14.7 Quantisation as an eigenvalue problem (Part 3)
      8. 14.8 Quantisation as an eigenvalue problem (Part 4)
      9. 14.9 Reflections
    6. Chapter 15 Reconciling matrix and wave mechanics
      1. 15.1 Schrödinger (1926d)
      2. 15.2 Lanczos (1926)
      3. 15.3 Born and Wiener’s operator formalism
      4. 15.4 Pauli’s letter to Jordan
      5. 15.5 Eckart and the operator calculus
      6. 15.6 Reconciling quantum mechanics and Bohr’s quantisation of angular momentum – the WKB approximation
      7. 15.7 Reflections
    7. Chapter 16 Spin and quantum statistics
      1. 16.1 Spin and the Landé $g$-factor
      2. 16.2 Heisenberg and the helium atom
      3. 16.3 Fermi–Dirac statistics – the Fermi approach
      4. 16.4 Fermi–Dirac statistics – the Dirac approach
      5. 16.5 Building spin into quantum mechanics – Pauli spin matrices
      6. 16.6 The Dirac equation and the theory of the electron
      7. 16.7 The discovery of the positron
    8. Chapter 17 The interpretation of quantum mechanics
      1. 17.1 Schrödinger’s interpretation (1926)
      2. 17.2 Born’s probabilistic interpretation of the wavefunction $ψ$ (1926)
      3. 17.3 Dirac–Jordan transformation theory
      4. 17.4 The mathematical completion of quantum mechanics
      5. 17.5 Heisenberg’s uncertainty principle
      6. 17.6 Ehrenfest’s theorem
      7. 17.7 The Copenhagen interpretation of quantum mechanics
    9. Chapter 18 The aftermath
      1. 18.1 The development of theory
      2. 18.2 The theory of quantum tunnelling
      3. 18.3 The splitting of the atom and the Cockcroft and Walton experiment
      4. 18.4 Discovery of the neutron
      5. 18.5 Discovery of nuclear fission
      6. 18.6 Pauli, the neutrino and Fermi’s theory of weak interactions
      7. 18.7 Cosmic rays and the discovery of elementary particles
      8. 18.8 Astrophysical applications
  12. Epilogue
  13. Notes
  14. References
  15. Name index
  16. Subject index