Contents -- Preface -- List of Figures -- 1. Introduction -- 2. The Classical Kepler Problem -- 2.1 Central Forces -- 2.2 The Laplace Vector -- 3. Symmetry of the Classical Problem -- 3.1 Lie Groups and Lie Algebras -- 3.2 Some Special Lie Algebras -- 3.3 Poisson Brackets -- 3.4 The Inverse Square Law -- 4. From Solar Systems to Atoms -- 4.1 Rutherford Scattering -- 4.2 Conservation of the Laplace Vector -- 4.3 The Differential Cross Section -- 5. The Bohr Model -- 5.1 Spectroscopic Series -- 5.2 The Postulates of the Model -- 5.3 The Predictions of the Model -- 5.4 Correction for Finite Nuclear Mass -- 6. Interpretation of the Quantum Rules -- 6.1 The Sommerfeld-Wilson Quantization Conditions -- 6.2 de Broglie's Wave Interpretation -- 7. Sommerfeld's Model for Non-Relativistic Electrons -- 7.1 Assumptions of the Model -- 7.2 Results of the Model for Non-Relativistic Hydrogen Atoms -- 7.3 The Eccentricity -- 8. Quantum Mechanics of Hydrogenic Atoms -- 8.1 Quantization -- 8.2 Quantum Mechanical Relation Between

12. Sommerfeld's Derivation of the Relativistic Energy Level Formula -- 12.1 Assumptions of the Model -- 12.2 The Energies of the Bound States -- 13. The Dirac Equation -- 13.1 The Hamiltonian -- 13.2 Total Angular Momentum -- 13.3 The Dirac Operator -- 13.4 A Complete Set of Mutually Commuting Operators -- 13.5 The Dirac Spinors -- 13.6 The Radial Equations in Polar Coordinates -- 14. The Primary Supersymmetry of the Dirac Equation -- 14.1 A Derivation of the Johnson-Lippmann Operator -- 14.2 Commutation and Anticommutation Relations of the Johnson-Lippmann Operator -- 14.3 Eccentricity -- 14.4 The Johnson-Lippmann Operator as the Generator of Supersymmetry -- 15. Extending the Solution Space -- 15.1 The Γ-Induced Radial Supersymmetry -- 15.2 The Supersymmetric Ground State in the Γ Representation -- 15.3 The General Solutions in the Γ Representation -- 16. A Different Extension of the Solution Space -- 16.1 The .-Induced Radial Supersymmetry -- 16.2 The Supersymmetric Ground State in the Representation -- 16.3 The General Solutions in the Representation -- 17. The Relation of the Solutions to Kramer's Equation -- 17.1 The Eigenvalue Problem for Traceless 2 × 2 Matrices -- 17.2 Eigenfunctions of the Operators G and -- 17.3 Kramer's Equation -- 18. Non-Relativistic Approximation -- 18.1 The Γ Representation -- 18.2 The Representation -- 19. Conclusions -- Appendices -- Appendix A. The Confluent Hypergeometric Function -- Appendix B. Orthogonality Relations of Hypergeometric Functions -- Appendix C. More Integrals Involving Hypergeometric Functions -- Appendix D. Normalization for the Γ-Induced Scheme -- Appendix E. Normalization for the -Induced Scheme -- Solutions to the Exercises -- Bibliography -- Index.