| |
| |
| Preface | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The Nature of the Problem | |
| |
| |
| |
| The Role of Symmetry | |
| |
| |
| |
| Abstract Group Theory | |
| |
| |
| |
| Definitions and Nomenclature | |
| |
| |
| |
| Illustrative Examples | |
| |
| |
| |
| Rearrangement Theorem | |
| |
| |
| |
| Cyclic Groups | |
| |
| |
| |
| Subgroups and Cosets | |
| |
| |
| |
| Example Groups of Finite Order | |
| |
| |
| |
| Conjugate Elements and Class Structure | |
| |
| |
| |
| Normal Divisors and Factor Groups | |
| |
| |
| |
| Class Multiplication | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| |
| Theory of Group Representations | |
| |
| |
| |
| Definitions | |
| |
| |
| |
| Proof of the Orthogonality Theorem | |
| |
| |
| |
| The Character of a Representation | |
| |
| |
| |
| Construction of Character Tables | |
| |
| |
| |
| Decomposition of Reducible Representations | |
| |
| |
| |
| Application of Representation Theory in Quantum Mechanics | |
| |
| |
| |
| Illustrative Representations of Abelian Groups | |
| |
| |
| |
| Basis Functions for Irreducible Representations | |
| |
| |
| |
| Direct-product Groups | |
| |
| |
| |
| Direct-product Representations within a Group | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| |
| Physical Applications of Group Theory | |
| |
| |
| |
| Crystal-symmetry Operators | |
| |
| |
| |
| The Crystallographic Point Groups | |
| |
| |
| |
| Irreducible Representations of the Point Groups | |
| |
| |
| |
| Elementary Representations of the Three-dimensional Rotation Group | |
| |
| |
| |
| Crystal-field Splitting of Atomic Energy Levels | |
| |
| |
| |
| Intermediate Crystal-field-splitting Case | |
| |
| |
| |
| Weak-crystal-field Case and Crystal Double Groups | |
| |
| |
| |
| Introduction of Spin Effects in the Medium-field Case | |
| |
| |
| |
| Group-theoretical Matrix-element Theorems | |
| |
| |
| |
| Selection Rules and Parity | |
| |
| |
| |
| Directed Valence | |
| |
| |
| |
| Application of Group Theory to Directed Valence | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| |
| Full Rotation Group and Angular Momentum | |
| |
| |
| |
| Rotational Transformation Properties and Angular Momentum | |
| |
| |
| |
| Continuous Groups | |
| |
| |
| |
| Representation of Rotations through Eulerian Angles | |
| |
| |
| |
| Homomorphism with the Unitary Group | |
| |
| |
| |
| Representations of the Unitary Group | |
| |
| |
| |
| Representation of the Rotation Group by Representations of the Unitary Group | |
| |
| |
| |
| Application of the Rotation-representation Matrices | |
| |
| |
| |
| Vector Model for Addition of Angular Momenta | |
| |
| |
| |
| The Wigner or Clebsch-Gordan Coefficients | |
| |
| |
| |
| Notation, Tabulations, and Symmetry Properties of the Wigner Coefficients | |
| |
| |
| |
| Tensor Operators | |
| |
| |
| |
| The Wigner-Eckart Theorem | |
| |
| |
| |
| The Racah Coefficients | |
| |
| |
| |
| Application of Racah Coefficients | |
| |
| |
| |
| The Rotation-Inversion Group | |
| |
| |
| |
| Time-reversal Symmetry | |
| |
| |
| |
| More General Invariances | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| |
| Quantum Mechanics of Atoms | |
| |
| |
| |
| Review of Elementary Atomic Structure and Nomenclature | |
| |
| |
| |
| The Hamiltonian | |
| |
| |
| |
| Approximate Eigenfunctions | |
| |
| |
| |
| Calculation of Matrix Elements between Determinantal Wavefunctions | |
| |
| |
| |
| Hartree-Fock Method | |
| |
| |
| |
| Calculation of L-S-term Energies | |
| |
| |
| |
| Evaluation of Matrix Elements of the Energy | |
| |
| |
| |
| Eigenfunctions and Angular-momentum Operations | |
| |
| |
| |
| Calculation of Fine Structure | |
| |
| |
| |
| Zeeman Effect | |
| |
| |
| |
| Magnetic Hyperfine Structure | |
| |
| |
| |
| Electric Hyperfine Structure | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| |
| Molecular Quantum Mechanics | |
| |
| |
| |
| Born-Oppenheimer Approximation | |
| |
| |
| |
| Simple Electronic Eigenfunctions | |
| |
| |
| |
| Irreducible Representations for Linear Molecules | |
| |
| |
| |
| The Hydrogen Molecule | |
| |
| |
| |
| Molecular Orbitals | |
| |
| |
| |
| Heitler-London Method | |
| |
| |
| |
| Orthogonal Atomic Orbitals | |
| |
| |
| |
| Group Theory and Molecular Orbitals | |
| |
| |
| |
| Selection Rules for Electronic Transitions | |
| |
| |
| |
| Vibration of Diatomic Molecules | |
| |
| |
| |
| Normal Modes in Polyatomic Molecules | |
| |
| |
| |
| Group Theory and Normal Modes | |
| |
| |
| |
| Selection Rules for Vibrational Transitions | |
| |
| |
| |
| Molecular Rotation | |
| |
| |
| |
| Effect of Nuclear Statistics on Molecular Rotation | |
| |
| |
| |
| Asymmetric Rotor | |
| |
| |
| |
| Vibration-Rotation Interaction | |
| |
| |
| |
| Rotation-Electronic Coupling | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| |
| Solid-state Theory | |
| |
| |
| |
| Symmetry Properties in Solids | |
| |
| |
| |
| The Reciprocal Lattice and Brillouin Zones | |
| |
| |
| |
| Form of Energy-band Wavefunctions | |
| |
| |
| |
| Crystal Symmetry and the Group of the k Vector | |
| |
| |
| |
| Pictorial Consideration of Eigenfunctions | |
| |
| |
| |
| Formal Consideration of Degeneracy and Compatibility | |
| |
| |
| |
| Group Theory and the Plane-wave Approximation | |
| |
| |
| |
| Connection between Tight- and Loose-binding Approximations | |
| |
| |
| |
| Spin-orbit Coupling in Band Theory | |
| |
| |
| |
| Time Reversal in Band Theory | |
| |
| |
| |
| Magnetic Crystal Groups | |
| |
| |
| |
| Symmetries of Magnetic Structures | |
| |
| |
| |
| The Landau Theory of Second-order Phase Transitions | |
| |
| |
| |
| Irreducible Representations of Magnetic Groups | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| Appendix | |
| |
| |
| |
| Review of Vectors, Vector Spaces, and Matrices | |
| |
| |
| |
| Character Tables for Point-symmetry Groups | |
| |
| |
| |
| Tables of c[superscript k] and a[superscript k] Coefficients for s, p, and d Electrons | |
| |
| |
| Index | |