| Preface |
| Introduction / 1： |
| The Nature of the Problem / 1-1： |
| The Role of Symmetry / 1-2： |
| Abstract Group Theory / 2： |
| Definitions and Nomenclature / 2-1： |
| Illustrative Examples / 2-2： |
| Rearrangement Theorem / 2-3： |
| Cyclic Groups / 2-4： |
| Subgroups and Cosets / 2-5： |
| Example Groups of Finite Order / 2-6： |
| Conjugate Elements and Class Structure / 2-7： |
| Normal Divisors and Factor Groups / 2-8： |
| Class Multiplication / 2-9： |
| Exercises |
| References |
| Theory of Group Representations / 3： |
| Definitions / 3-1： |
| Proof of the Orthogonality Theorem / 3-2： |
| The Character of a Representation / 3-3： |
| Construction of Character Tables / 3-4： |
| Decomposition of Reducible Representations / 3-5： |
| Application of Representation Theory in Quantum Mechanics / 3-6： |
| Illustrative Representations of Abelian Groups / 3-7： |
| Basis Functions for Irreducible Representations / 3-8： |
| Direct-product Groups / 3-9： |
| Direct-product Representations within a Group / 3-10： |
| Physical Applications of Group Theory / 4： |
| Crystal-symmetry Operators / 4-1： |
| The Crystallographic Point Groups / 4-2： |
| Irreducible Representations of the Point Groups / 4-3： |
| Elementary Representations of the Three-dimensional Rotation Group / 4-4： |
| Crystal-field Splitting of Atomic Energy Levels / 4-5： |
| Intermediate Crystal-field-splitting Case / 4-6： |
| Weak-crystal-field Case and Crystal Double Groups / 4-7： |
| Introduction of Spin Effects in the Medium-field Case / 4-8： |
| Group-theoretical Matrix-element Theorems / 4-9： |
| Selection Rules and Parity / 4-10： |
| Directed Valence / 4-11： |
| Application of Group Theory to Directed Valence / 4-12： |
| Full Rotation Group and Angular Momentum / 5： |
| Rotational Transformation Properties and Angular Momentum / 5-1： |
| Continuous Groups / 5-2： |
| Representation of Rotations through Eulerian Angles / 5-3： |
| Homomorphism with the Unitary Group / 5-4： |
| Representations of the Unitary Group / 5-5： |
| Representation of the Rotation Group by Representations of the Unitary Group / 5-6： |
| Application of the Rotation-representation Matrices / 5-7： |
| Vector Model for Addition of Angular Momenta / 5-8： |
| The Wigner or Clebsch-Gordan Coefficients / 5-9： |
| Notation, Tabulations, and Symmetry Properties of the Wigner Coefficients / 5-10： |
| Tensor Operators / 5-11： |
| The Wigner-Eckart Theorem / 5-12： |
| The Racah Coefficients / 5-13： |
| Application of Racah Coefficients / 5-14： |
| The Rotation-Inversion Group / 5-15： |
| Time-reversal Symmetry / 5-16： |
| More General Invariances / 5-17： |
| Quantum Mechanics of Atoms / 6： |
| Review of Elementary Atomic Structure and Nomenclature / 6-1： |
| The Hamiltonian / 6-2： |
| Approximate Eigenfunctions / 6-3： |
| Calculation of Matrix Elements between Determinantal Wavefunctions / 6-4： |
| Hartree-Fock Method / 6-5： |
| Calculation of L-S-term Energies / 6-6： |
| Evaluation of Matrix Elements of the Energy / 6-7： |
| Eigenfunctions and Angular-momentum Operations / 6-8： |
| Calculation of Fine Structure / 6-9： |
| Zeeman Effect / 6-10： |
| Magnetic Hyperfine Structure / 6-11： |
| Electric Hyperfine Structure / 6-12： |
| Molecular Quantum Mechanics / 7： |
| Born-Oppenheimer Approximation / 7-1： |
| Simple Electronic Eigenfunctions / 7-2： |
| Irreducible Representations for Linear Molecules / 7-3： |
| The Hydrogen Molecule / 7-4： |
| Molecular Orbitals / 7-5： |
| Heitler-London Method / 7-6： |
| Orthogonal Atomic Orbitals / 7-7： |
| Group Theory and Molecular Orbitals / 7-8： |
| Selection Rules for Electronic Transitions / 7-9： |
| Vibration of Diatomic Molecules / 7-10： |
| Normal Modes in Polyatomic Molecules / 7-11： |
| Group Theory and Normal Modes / 7-12： |
| Selection Rules for Vibrational Transitions / 7-13： |
| Molecular Rotation / 7-14： |
| Effect of Nuclear Statistics on Molecular Rotation / 7-15： |
| Asymmetric Rotor / 7-16： |
| Vibration-Rotation Interaction / 7-17： |
| Rotation-Electronic Coupling / 7-18： |
| Solid-state Theory / 8： |
| Symmetry Properties in Solids / 8-1： |
| The Reciprocal Lattice and Brillouin Zones / 8-2： |
| Form of Energy-band Wavefunctions / 8-3： |
| Crystal Symmetry and the Group of the k Vector / 8-4： |
| Pictorial Consideration of Eigenfunctions / 8-5： |
| Formal Consideration of Degeneracy and Compatibility / 8-6： |
| Group Theory and the Plane-wave Approximation / 8-7： |
| Connection between Tight- and Loose-binding Approximations / 8-8： |
| Spin-orbit Coupling in Band Theory / 8-9： |
| Time Reversal in Band Theory / 8-10： |
| Magnetic Crystal Groups / 8-11： |
| Symmetries of Magnetic Structures / 8-12： |
| The Landau Theory of Second-order Phase Transitions / 8-13： |
| Irreducible Representations of Magnetic Groups / 8-14： |
| Appendix |
| Review of Vectors, Vector Spaces, and Matrices / A： |
| Character Tables for Point-symmetry Groups / B： |
| Tables of c[superscript k] and a[superscript k] Coefficients for s, p, and d Electrons / C： |
| Index |
| Preface |
| Introduction / 1： |
| The Nature of the Problem / 1-1： |
