The Quantum Theory―Origins and Ideas: A Historical Primer for Physics Students [1 ed.] 9783030792688, 9783030792671

Table of contents :
Preface
Contents
1 The Atomic Theory
1.1 Introduction
1.2 Atoms in Ancient and Early Modern Theories
1.2.1 Ancient Theories
1.2.2 Early European Thoughts
1.2.3 Atomic Motion and Pressure
1.2.4 Boscovich's Atomic Model
1.3 Interactions
1.3.1 Atoms and the Voltaic Pile
1.3.2 Phlogiston and Caloric
1.3.3 Heat and Thermodynamics
1.3.4 Kinetic Theory
1.4 Gas Discharges and Cathode Rays
1.4.1 Rarefied Gases
1.4.2 Cathode Rays
1.4.3 Thomson's Experiment
1.5 Statistical Mechanics
1.5.1 Gibbs' Perspective
1.5.2 Ensembles of Systems
1.5.3 Statistics of the H-Theorem
1.6 Thomson's Atomic Model
1.7 Nagaoka's Atomic Model
1.8 X-Rays and Electron Number
1.8.1 Barkla
1.8.2 Diffraction
1.8.3 The Braggs
1.9 Rutherford and the Nucleus
1.10 Summary
2 Discovery of the Quantum
2.1 Introduction
2.2 Planck and the Second Law
2.3 Blackbody Radiation
2.3.1 Formulae for Radiation Intensity
2.3.2 Sources of Radiation
2.3.3 Thermodynamics and Radiation
2.3.4 Measurements in the Infrared
2.4 Probability and the Quantum
2.5 Planck's Nobel Lecture
2.6 Summary
3 Electrodynamics and Matter
3.1 Introduction
3.2 Planck's Second Theory
3.3 Einstein and Photons
3.3.1 Regarding One of the Difficulties Encountered by the Theory of “Black Radiation”
3.3.2 Regarding the Planck Result for Elementary Quanta
3.3.3 Regarding the Entropy of the Radiation
3.3.4 Limiting Form of the Entropy for Low Density Monochromatic Radiation
3.3.5 Molecular Theoretical Considerations Regarding the Dependence of the Entropy of Gases and Weak Solutions on Volume
3.3.6 Interpretation of the Expression for the Dependence of the Entropy of Monochromatic Radiation on Volume According to the Boltzmann Principle
3.3.7 Regarding Stokes Law
3.3.8 Regarding the Production of Cathode Rays by Illumination of Solid Surfaces
3.3.9 Regarding the Ionization of a Gas by Ultraviolet Light
3.4 Summary
4 Quantum Atoms
4.1 Introduction
4.2 Niels Bohr
4.2.1 Doctorate and Cambridge
4.2.2 Bohr's Model
4.3 Arnold Sommerfeld
4.3.1 Thoughts and Ideas
4.3.2 Zeeman Effect
4.3.3 Beyond Models
4.4 Summary
5 Experimental Evidence
5.1 Introduction
5.2 Bohr Model
5.2.1 Ionized Helium
5.2.2 Moseley
5.2.3 Franck and Hertz
5.3 The Einstein Photon
5.3.1 Experiments by Millikan
5.3.2 Compton's Experiments
5.4 Bohr and the Photon
5.4.1 Ideas of Bohr, Kramers, and Slater
5.4.2 Bothe and Geiger's Experiment
5.4.3 Experiment of Compton and Simon
5.5 Spatial Quantization: Stern and Gerlach
5.6 Summary
6 De Broglie's Particle Wave
6.1 Introduction
6.2 De Broglie's Thesis
6.3 The Phase Wave
6.3.1 The Relation Between the Quantum and Relativity Theories
6.3.2 Phase and Group Velocities
6.3.3 Phase Waves in Space-Time
6.4 Connections
6.4.1 Defense of the Thesis
6.4.2 Influences
6.5 Davisson–Germer Experiment
6.6 Summary
7 Göttingen Quantum Theory
7.1 Introduction
7.2 Background
7.3 Matrix Mechanics
7.3.1 Kramers and Heisenberg
7.3.2 Heisenberg
7.3.3 Born and Jordan
7.3.4 Born, Heisenberg, and Jordan
7.3.5 Enter Dirac
7.4 Summary
8 Schrödinger's Wave Theory
8.1 Introduction
8.2 Schrödinger's First Correspondence
8.3 Physical Review December 1926
8.3.1 An Analogy: Mechanics and Optics
8.3.2 Analogy and ``Undulatory'' Mechanics
8.3.3 Significance of Wavelength
8.3.4 Application to the Hydrogen Atom
8.3.5 Discrete Characteristic Frequencies
8.3.6 Intensity of Emitted Light
8.3.7 Wave Equation from a Variational Principle
8.3.8 Physical Meaning of the Wave Equation
8.3.9 Non-conservative Systems and Dispersion
8.3.10 Relativity and the Magnetic Field
8.4 Summary
9 Spin and Its Interpretation
9.1 Introduction
9.2 Spin of the Electron
9.3 Interpretation of the Wave Function
9.4 Copenhagen Interpretation
9.5 Summary
10 Connecting the Matrix and Wave Theories
10.1 Introduction
10.2 Symbolic Method and Representation
10.2.1 Schrödinger Picture
10.2.2 Heisenberg Picture
10.3 Summary
11 Epilogue
Appendix A Hamilton and Fermat
A.1 W and φ Surfaces
A.2 Variational Principle
Appendix B Schrödinger's Variation
Appendix C Schwarz Inequality
Appendix D Heisenberg's Principle
Appendix E Displacement Operator
Appendix References
Index