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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 Representationsof 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 PrimitiveTranslations

13. The Irreducible Representations of Space GroupsReferences

3. Connection of Quantum Mechanics withGroup Theory

1. The Effect of an Orthogonal Coordinate Transformation onthe Vectors of a Hilbert Space

2. The Symmetry Group of the Schr¨odinger Equation

3. The Fundamental Theorem for Functionsand OperatorsTransforming Irreducibly

4. The Construction of Functions TransformingIrreducibly

5. The Full Rotational Group and the Quantum Theoryof Angular Momentum

6. The Spin of the Electron and the Double ValuedRepresentations

7. The Kramers'Degeneracy

8. The Symmetric Group of the Hamiltonian and the PauliPrincipleReferences

4. The Hydrogen Atom

1. The Unperturbed Hamiltonian

2. The Spin-Orbit Interaction

3. The Zeeman Interaction

4. Group Theoretical Considerations for the H AtomReferences

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 Equivalenceof Electrons and Holes

6. The Spin-Orbit Splitting of Terms

7. An Example of Spin-Orbit and Zeeman SplittingReferences

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 PropertiesofMagnetic Ions

4. The Crystalline Field HypothesisReferences

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 DifferentSymmetriesReferences

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 ofTransition Metal Ions Levels in an OctahedralCrystal FieldReferences

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 MagneticIons 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 ConstructionofMolecularOrbitals

5. The Formation of Hybrids

6. Hybrids of the Central Ion in a TetrahedralComplex AB4

7. Hybrids of the Central Ion in an OctahedralComplex AB6

8. The Combinations of Ligand Orbitals in anABn Complex

9. The Energy Levels of an ABn ComplexReferences

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 theNormal 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 Coordinatesof a Tetrahedral Complex AB4

8. The Normal Modes and the Symmetry Coordinatesof an Octahedral Complex AB6References

13. Lattice Vibrations

1. The Geometry of Crystalline Solids

2. Lattice Vibrations of an Infinite Crystal withOne AtomPer Unit Cell

3. Lattice Vibrations of a Finite Crystal withOne AtomPer Unit Cell

4. Lattice Vibrations of a Crystal with More ThanOne AtomPer Unit Cell

5. Thermodynamics of Phonons

6. Phonons and Photons. Similarities and DifferencesReferences

14. The Ion-Photon Interaction: Absorption andEmission 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 Betweenan Atomic System and the Electromagnetic FieldReferences

15. The Judd-Ofelt Theory

1. Motivation

2. General Considerations

3. The Theory

4. ApplicationsReferences

16. The Ion-Vibration Interaction. RadiationlessProcesses, Thermal Shift, and Broadeningof 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 ShiftReferences

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 Ionsin Perfect Crystals

7. Selection Rules for Vibronic Transitions Dueto Magnetic Impurities in CrystalsReferences

18. Energy Transfer Among Ions in Solids

1. Quantum-Mechanical Treatment of the InteractionsAmong 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 ExcitationAmong DonorsReferences

19. Absorption Spectra of Magnetic Ions in Crystals

1. The A and B Coefficients as Related to Magnetic Ionsin 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 UnderContinuous Excitation

2. The Response of Fluorescent Systemsto Transient Excitation

3. General Properties of the Fluorescence Decaysin aMultilevel System

4. Interactions of Magnetic Ions and Their Effectson the FluorescenceOutput

5. The Factors Affecting the Fluorescence Emission

6. Fluorescence of Magnetic Ions in CrystalsReferences

21. Elements of Laser Theory

1. Laser Conditions

2. Examples of Ionic Solid State LasersReferences

Subject Index