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: |
The Role of Symmetry / 1-2: |
Abstract Group Theory / 2: |
Definitions and Nomenclature / 2-1: |