Preface to the Second Edition
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

Preface to the Second Edition
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
　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
　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
　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
　1. Bonding in Crystals
　2. The Ionic Bond in Crystals
　3. Electronic Configurations and Properties　ofMagnetic Ions
　4. The Crystalline Field Hypothesis　References
7. The Weak Field Scheme
　1. The Hamiltonian of the Free Ion
　2. The Crystal Field Perturbation
　3. Application of theWeak Field Scheme
　4. Splittings of J Levels in Fields of Different　Symmetries　References
8. The Medium Field Scheme
　1. The Hamiltonian of the Free Ion
　2. The Crystal Field Perturbation
　3. The Spin-Orbit Interaction
　4. An Application of the Medium Field Scheme
　5. The Method of Operator Equivalents: The Splitting of　Transition Metal Ions Levels in an Octahedral　Crystal Field　References
9. The Strong Field Scheme
　1. The Unperturbed Hamiltonian
　2. The Crystal Field Perturbation
　3. The Electrostatic Interaction
　4. The Spin-Orbit Interaction
10. Covalent Bonding and Its Effect on Magnetic　Ions in Crystals
　1. The Relevance of Covalent Bonding
　2. The Formation of Molecular Orbitals
　3. Example of Molecular Orbitals Formation
　4. The Use of Projection Operators in the Construction　ofMolecularOrbitals
　5. The Formation of Hybrids
　6. Hybrids of the Central Ion in a Tetrahedral　Complex AB4
　7. Hybrids of the Central Ion in an Octahedral　Complex AB6
　8. The Combinations of Ligand Orbitals in an　ABn Complex
　9. The Energy Levels of an ABn Complex　References
11. The Quantum Theory of the Radiation Field
　1. The Classical Electromagnetic Field
　2. The Quantum Theory of the Electromagnetic Field
12. Molecular Vibrations
　1. The Classical Theory of Molecular Vibrations
　2. The Symmetry of the Molecules and the　Normal Coordinates
　3. How to Find the Normal Modes of Vibration
　4. The Use of Symmetry Coordinates
　5. The Quantum Theory of Molecular Vibrations
　6. The Selection Rules for Infrared and Raman Transitions, The Fermi Resonance
　7. The Normal Modes and the Symmetry Coordinates　of a Tetrahedral Complex AB4
　8. The Normal Modes and the Symmetry Coordinates　of an Octahedral Complex AB6　References
13. Lattice Vibrations
　1. The Geometry of Crystalline Solids
　2. Lattice Vibrations of an Infinite Crystal with　One AtomPer Unit Cell
　3. Lattice Vibrations of a Finite Crystal with　One AtomPer Unit Cell
　4. Lattice Vibrations of a Crystal with More Than　One AtomPer Unit Cell
　5. Thermodynamics of Phonons
　6. Phonons and Photons. Similarities and Differences　References
14. The Ion-Photon Interaction: Absorption and　Emission of Radiation
　1. The Ion-Radiation Interaction
　2. The Expansion of the Interaction Hamiltonian:　Different Types of Radiation
　3. The Density of Final States
　4. The Transition Probability Per Unit Time
　5. Dipole Radiation
　6. Selection Rules for Radiative Transitions
　7. About the Intensities of Radiative Transitions
　8. The Static Effects of the Interaction Between　an Atomic System and the Electromagnetic Field　References
15. The Judd-Ofelt Theory
　1. Motivation
　2. General Considerations
　3. The Theory
　4. Applications　References
16. The Ion-Vibration Interaction. Radiationless　Processes, Thermal Shift, and Broadening　of Sharp Lines
　1. The Ion-Vibration Interaction
　2. Radiationless Processes in Crystals
　3. Different Types of Line Broadening Mechanisms:　Lorentzian and Gaussian Line Shapes
　4. Theory of Thermal Broadening of Sharp Lines
　5. Theory of Thermal Line Shift　References
17. Vibrational-Electronic Interaction and Spectra
　1. Introduction
　2. Ion-Vibration Interaction in Molecular Complexes
　3. Vibronic Spectra of Molecular Complexes
　4. Space Groups and Lattice Vibrations
　5. Lattice Absorption in Perfect Crystals
　6. Phonon Activation Due to Impurity Ions　in Perfect Crystals
　7. Selection Rules for Vibronic Transitions Due　to Magnetic Impurities in Crystals　References
18. Energy Transfer Among Ions in Solids
　1. Quantum-Mechanical Treatment of the Interactions　Among Atoms
　2. Different Types of Interactions
　3. Modes of Excitation and Transfer
　4. Energy Transfer with No Migration of Excitation Among Donors
　5. Energy Transfer with Migration of Excitation　Among Donors　References
19. Absorption Spectra of Magnetic Ions in Crystals
　1. The A and B Coefficients as Related to Magnetic Ions　in Crystals
　2. General Properties of Absorption Spectra
　3. Absorption Spectra of Magnetic Ions in Crystals
　4. The Effects of Temperature on Absorption Spectra
　5. Excited State Absorption References
20. Fluorescence Spectra of Magnetic Ions in Crystals
　1. The Fluorescence Emission of Magnetic Ions Under　Continuous Excitation
　2. The Response of Fluorescent Systems　to Transient Excitation
　3. General Properties of the Fluorescence Decays　in aMultilevel System
　4. Interactions of Magnetic Ions and Their Effects　on the FluorescenceOutput
　5. The Factors Affecting the Fluorescence Emission
　6. Fluorescence of Magnetic Ions in Crystals　References
21. Elements of Laser Theory
　1. Laser Conditions
　2. Examples of Ionic Solid State Lasers　References
Subject Index