1．Elements of Quantum Mechanics 1
1．Review of Classical Mechanics 1
2．Vector Spaces and Linear Operators 4
3．Basic Postulates of Quantum Mechanics 10
4．Compatible Observables and Complete Set of Commuting Operators 13
5．Form of the Operators 15
6．Matrix Formalism and Transformation Theory 20
7．General Theory of Angular Momentum 29
8．Time-Independent Perturbation Theory 35
9．Time-Dependent Perturbation Theory 42
References 48
2．Elements of Group Theory 49
1．Properties of a Group 49
2．Classes 51
3．Theory of Representations 53
4．Schur's Lemma and Orthogonality Relations 58
5 Characters of a Group 61
6．Properties of the Irreducible Representations of a Group 64
7．The Direct Product Representation 65
8．Product Groups and Their Representations 66
9．Summary of Rules 68
10 ．Groups of Real Orthogonal Matrices 69
11．Space Groups and Symmetry of Crystalline Solids 75
12．The Irreducible Representations of a Group of Primitive Translations 92
13．The Irreducible Representations of Space Groups 95
References 113
3．Connection of Quantum Mechanics with Group Theory 115
1．The Effect of an Orthogonal Coordinate Transformation on the Vectors of a Hilbert Space 115
2．The Symmetry Group of the Schr？dinger Equation 117
3．The Fundamental Theorem for Functions and Operators Transforming Irreducibly 121
4．The Construction of Functions Transforming Irreducibly 124
5．The Full Rotational Group and the Quantum Theory of Angular Momentum 127
6．The Spin of the Electron and the Double Valued Representations 137
7．The Kramers'Degeneracy 142
8．The Symmetric Group of the Hamiltonian and the Pauli Principle 148
References 154
4．The Hydrogen Atom 155
1．The Unperturbed Hamiltonian 155
2．The Spin-Orbit Interaction 157
3．The Zeeman Interaction 160
4．Group Theoretical Considerations for the H Atom 162
References 164
5．The Complex Atom：Multiplet Theory 165
1．The Helium Atom 165
2．The Many Electron Atom 169
3．Group Theoretical Considerations for a Complex Atom 176
4．The Energies of Spectral Terms 180
5．Hund's Rules and the Principle of Equivalence of Electrons and Holes 188
6．The Spin-Orbit Splitting of Terms 190
7．An Example of Spin-Orbit and Zeeman Splitting 193
References 195
6．The Magnetic Ion in a Crystal：The Role of Symmetry 197
1．Bonding in Crystals 197
2．The Ionic Bond in Crystals 198
3．Electronic Configurations and Properties of Magnetic Ions 201
4．The Crystalline Field Hypothesis 212
References 216
7．The Weak Field Scheme 217
1．The Hamiltonian of the Free Ion 217
2．The Crystal Field Perturbation 218
3．Application of the Weak Field Scheme 219
4．Splittings of J Levels in Fields of Different Symmetries 223
References 223
8．The Medium Field Scheme 225
1．The Hamiltonian of the Free Ion 225
2．The Crystal Field Perturbation 227
3．The Spin-Orbit Interaction 228
4．An Application ofthe Medium Field Scheme 228
5．The Method of Operator Equivalents：The Splitting of Transition Metal Ions Levels in an Octahedral Crystal Field 230
References 235
9．The Strong Field Scheme 237
1．The Unperturbed Hamiltonian 237
2．The Crystal Field Perturbation 239
3．The Electrostatic Interaction 240
4．The Spin-Orbit Interaction 241
10．Covalent Bonding and Its Effect on Magnetic Ions in Crystals 243
1．The Relevance of Covalent Bonding 243
2．The Formation of Molecular Orbitals 244
3．Example of Molecular Orbitals Formation 246
4．The Use of Projection Operators in the Construction of Molecular Orbitals 258
5．The Formation of Hybrids 262
6．Hybrids of the Central Ion in a Tetrahedral Complex AB4 267
7．Hybrids of the Central Ion in an Octahedral Complex AB6 269
8．The Combinations of Ligand Orbitals in an ABn Complex 271
9．The Energy Levels of an ABn Complex 274
References 282
11．The Quantum Theory of the Radiation Field 283
1．The Classical Electromagnetic Field 283
2．The Quantum Theory of the Electromagnetic Field 286
12．Molecular Vibrations 295
1．The Classical Theory of Molecular Vibrations 295
2．The Symmetry of the Molecules and the Normal Coordinates 299
3．How to Find the Normal Modes of Vibration 300
4．The Use of Symmetry Coordinates 303
5．The Quantum Theory of Molecular Vibrations 307
6．The Selection Rules for Infrared and Raman Transitions,The Fermi Resonance 309
7．The Normal Modes and the Symmetry Coordinates of a Tetrahedral Complex AB4 312
8．The Normal Modes and the Symmetry Coordinates of an Octahedral Complex AB6 315
References 321
13．Lattice Vibrations 323
1．The Geometry of Crystalline Solids 323
2．Lattice Vibrations of an Infinite Crystal with One Atom Per Unit Cell 326
3．Lattice Vibrations of a Finite Crystal with One Atom Per Unit Cell 329
4．Lattice Vibrations of a Crystal with More Than One Atom Per Unit Cell 336
5．Thermodynamics of Phonons 339
6．Phonons and Photons.Similarities and Differences 346
References 347
14．The Ion-Photon Interaction：Absorption and Emission of Radiation 349
1．The Ion-Radiation Interaction 349
2．The Expansion of the Interaction Hamiltonian：Different Types of Radiation 351
3．The Density of Final States 353
4．The Transition Probability Per Unit Time 354
5．Dipole Radiation 356
6．Selection Rules for Radiative Transitions 358
7．About the Intensities of Radiative Transitions 369
8．The Static Effects of the Interaction Between an Atomic System and the Electromagnetic Field 373
References 374
15．The Judd-Ofelt Theory 375
1．Motivation 375
2．General Considerations 376
3．The Theory 377
4．Applications 381
References 382
16．The Ion-Vibration Interaction.Radiationless Processes,Thermal Shift,and Broadening of Sharp Lines 385
1．The Ion-Vibration Interaction 385
2．Radiationless Processes in Crystals 387
3．Different Types of Line Broadening Mechanisms：Lorentzian and Gaussian Line Shapes 402
4．Theory of Thermal Broadening of Sharp Lines 413
5．Theory of Thermal Line Shift 418
References 423
17．Vibrational-Electronic Interaction and Spectra 425
1．Introduction 425
2．Ion-Vibration Interaction in Molecular Complexes 425
3．Vibronic Spectra of Molecular Complexes 427
4．Space Groups and Lattice Vibrations 438
5．Lattice Absorption in Perfect Crystals 445
6．Phonon Activation Due to Impurity Ions in Perfect Crystals 447
7．Selection Rules for Vibronic Transitions Due to Magnetic Impurities in Crystals 450
References 452
18．Energy Transfer Among Ions in Solids 455
1．Quantum-Mechanical Treatment of the Interactions Among Atoms 455
2．Different Types of Interactions 469
3．Modes of Excitation and Transfer 478
4．Energy Transfer with No Migration of Excitation Among Donors 482
5．Energy Transfer with Migration of Excitation Among Donors 495
References 514
19．Absorption Spectra of Magnetic Ions in Crystals 517
1．The A and B Coefficients as Related to Magnetic Ions in Crystals 517
2．General Properties of Absorption Spectra 520
3．Absorption Spectra of Magnetic Ions in Crystals 526
4．The Effects of Temperature on Absorption Spectra 532
5．Excited State Absorption 541
References 544
20．Fluorescence Spectra of Magnetic Ions in Crystals 547
1．The Fluorescence Emission of Magnetic Ions Under Continuous Excitation 547
2．The Response of Fluorescent Systems to Transient Excitation 553
3．General Properties of the Fluorescence Decays in a Multilevel System 558
4．Interactions of Magnetic Ions and Their Efiects on the Fluorescence Output 562
5．The Factors Affecting the Fluorescence Emission 564
6．Fluorescence of Magnetic Ions in Crystals 573
References 578
21．Elements of Laser Theory 583
1．Laser Conditions 583
2．Examples of Ionic Solid State Lasers 598
References 605
Subject Index 607