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Preface | |

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Introduction | |

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The Nature of the Problem | |

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The Role of Symmetry | |

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Abstract Group Theory | |

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Definitions and Nomenclature | |

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Illustrative Examples | |

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Rearrangement Theorem | |

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Cyclic Groups | |

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Subgroups and Cosets | |

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Example Groups of Finite Order | |

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Conjugate Elements and Class Structure | |

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Normal Divisors and Factor Groups | |

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Class Multiplication | |

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Exercises | |

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References | |

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Theory of Group Representations | |

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Definitions | |

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Proof of the Orthogonality Theorem | |

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The Character of a Representation | |

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Construction of Character Tables | |

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Decomposition of Reducible Representations | |

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Application of Representation Theory in Quantum Mechanics | |

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Illustrative Representations of Abelian Groups | |

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Basis Functions for Irreducible Representations | |

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Direct-product Groups | |

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Direct-product Representations within a Group | |

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Exercises | |

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References | |

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Physical Applications of Group Theory | |

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Crystal-symmetry Operators | |

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The Crystallographic Point Groups | |

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Irreducible Representations of the Point Groups | |

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Elementary Representations of the Three-dimensional Rotation Group | |

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Crystal-field Splitting of Atomic Energy Levels | |

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Intermediate Crystal-field-splitting Case | |

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Weak-crystal-field Case and Crystal Double Groups | |

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Introduction of Spin Effects in the Medium-field Case | |

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Group-theoretical Matrix-element Theorems | |

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Selection Rules and Parity | |

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Directed Valence | |

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Application of Group Theory to Directed Valence | |

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Exercises | |

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References | |

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Full Rotation Group and Angular Momentum | |

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Rotational Transformation Properties and Angular Momentum | |

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Continuous Groups | |

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Representation of Rotations through Eulerian Angles | |

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Homomorphism with the Unitary Group | |

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Representations of the Unitary Group | |

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Representation of the Rotation Group by Representations of the Unitary Group | |

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Application of the Rotation-representation Matrices | |

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Vector Model for Addition of Angular Momenta | |

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The Wigner or Clebsch-Gordan Coefficients | |

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Notation, Tabulations, and Symmetry Properties of the Wigner Coefficients | |

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Tensor Operators | |

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The Wigner-Eckart Theorem | |

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The Racah Coefficients | |

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Application of Racah Coefficients | |

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The Rotation-Inversion Group | |

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Time-reversal Symmetry | |

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More General Invariances | |

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Exercises | |

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References | |

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Quantum Mechanics of Atoms | |

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Review of Elementary Atomic Structure and Nomenclature | |

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The Hamiltonian | |

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Approximate Eigenfunctions | |

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Calculation of Matrix Elements between Determinantal Wavefunctions | |

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Hartree-Fock Method | |

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Calculation of L-S-term Energies | |

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Evaluation of Matrix Elements of the Energy | |

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Eigenfunctions and Angular-momentum Operations | |

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Calculation of Fine Structure | |

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Zeeman Effect | |

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Magnetic Hyperfine Structure | |

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Electric Hyperfine Structure | |

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Exercises | |

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References | |

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Molecular Quantum Mechanics | |

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Born-Oppenheimer Approximation | |

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Simple Electronic Eigenfunctions | |

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Irreducible Representations for Linear Molecules | |

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The Hydrogen Molecule | |

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Molecular Orbitals | |

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Heitler-London Method | |

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Orthogonal Atomic Orbitals | |

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Group Theory and Molecular Orbitals | |

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Selection Rules for Electronic Transitions | |

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Vibration of Diatomic Molecules | |

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Normal Modes in Polyatomic Molecules | |

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Group Theory and Normal Modes | |

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Selection Rules for Vibrational Transitions | |

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Molecular Rotation | |

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Effect of Nuclear Statistics on Molecular Rotation | |

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Asymmetric Rotor | |

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Vibration-Rotation Interaction | |

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Rotation-Electronic Coupling | |

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Exercises | |

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References | |

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Solid-state Theory | |

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Symmetry Properties in Solids | |

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The Reciprocal Lattice and Brillouin Zones | |

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Form of Energy-band Wavefunctions | |

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Crystal Symmetry and the Group of the k Vector | |

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Pictorial Consideration of Eigenfunctions | |

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Formal Consideration of Degeneracy and Compatibility | |

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Group Theory and the Plane-wave Approximation | |

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Connection between Tight- and Loose-binding Approximations | |

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Spin-orbit Coupling in Band Theory | |

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Time Reversal in Band Theory | |

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Magnetic Crystal Groups | |

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Symmetries of Magnetic Structures | |

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The Landau Theory of Second-order Phase Transitions | |

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Irreducible Representations of Magnetic Groups | |

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Exercises | |

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References | |

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Appendix | |

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Review of Vectors, Vector Spaces, and Matrices | |

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Character Tables for Point-symmetry Groups | |

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Tables of c[superscript k] and a[superscript k] Coefficients for s, p, and d Electrons | |

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Index | |