Preface to the Second Edition vii 1. Elements of Quantum Mechanics 1. Review of ClassicalMechanics 2. Vector Spaces and Linear Operators 3. Basic Postulates of Quantum Mechanics 4. Compatible Observables and Complete Set of Commuting Operators 5. Formof the Operators 6. Matrix Formalism and Transformation Theory 7. General Theory of Angular Momentum 8. Time-Independent Perturbation Theory 9. Time-Dependent Perturbation Theory References 2. Elements of Group Theory 1. Properties of a Group 2. Classes 3. Theory of Representations 4. Schur's Lemma and Orthogonality Relations 5. Characters of a Group 6. Properties of the Irreducible Representations of a Group 7. The Direct Product Representation 8. Product Groups and Their Representations 9. Summary of Rules 10. Groups of Real Orthogonal Matrices 11. Space Groups and Symmetry of Crystalline Solids 12. The Irreducible Representations of a Group of Primitive Translations 13. The Irreducible Representations of Space Groups References 3. Connection of Quantum Mechanics with Group Theory 115 1. The Effect of an Orthogonal Coordinate Transformation on the Vectors of a Hilbert Space 2. The Symmetry Group of the Schr¨odinger Equation 3. The Fundamental Theorem for Functions and OperatorsTransforming Irreducibly 4. The Construction of Functions Transforming Irreducibly 5. The Full Rotational Group and the Quantum Theory of Angular Momentum 6. The Spin of the Electron and the Double Valued Representations 7. The Kramers'Degeneracy 8. The Symmetric Group of the Hamiltonian and the Pauli Principle References 4. The Hydrogen Atom 155 1. The Unperturbed Hamiltonian 2. The Spin-Orbit Interaction 3. The Zeeman Interaction 4. Group Theoretical Considerations for the H Atom References 5. The Complex Atom: Multiplet Theory 165 1. The Helium Atom 2. The Many Electron Atom 3. Group Theoretical Considerations for a Complex Atom 4. The Energies of Spectral Terms 5. Hund's Rules and the Principle of Equivalence of Electrons and Holes 6. The Spin-Orbit Splitting of Terms 7. An Example of Spin-Orbit and Zeeman Splitting References …… 6. The Magnetic Ion in a Crystal: The Role of Symmetry 216 7. The Weak Field Scheme 8. The Medium Field Scheme 9. The Strong Field Scheme 10. Covalent Bonding and Its Effect on MagneticIons in Crystals 11. The Quantum Theory of the Radiation Field 12. Molecular Vibrations 13. Lattice Vibrations 14. The Ion-Photon Interaction: Absorption and Emission of Radiation 15. The Judd-Ofelt Theory 16. The Ion-Vibration Interaction. Radiationless Processes， Thermal Shift， and Broadening of Sharp Lines 17. Vibrational-Electronic Interaction and Spectra 18. Energy Transfer Among Ions in Solids 19. Absorption Spectra of Magnetic Ions in Crystals 20. Fluorescence Spectra of Magnetic Ions in Crystals 21. Elements of Laser Theory References Subject Index
