Theory of Groups and Its Application to Physical Problems

Preface to American EditionPreface to First EditionI. Groups Group Postulates Displacement of a Rigid Body Symmetry Operations Point Groups Space GroupsII. One-Dimensional Lattice Symmetry of the Lattice One-Dimensional Motives Two-Dimensional Motives Three-Dimensional MotivesIII. Lattices in Two Dimensions Symmetry of the Lattices Two-Dimensional Motives Three-Dimensional MotivesIV. Some Properties of Groups Abstract Groups Subgroups Classes of Conjugate Elements Self-Conjugate Subgroups Factor Groups Permutation Groups Isomorphous Groups Direct Product GroupsV. Matrix Groups Matrices Linear Transformations Equivalent Matrices Reducible and Irreducible Matrix Representations of Groups Kronecker Square and Symmetrized Kronecker Square Representations Kronecker Direct Product of Two RepresentationsVI. The Wave Equation and Its Properties Vibrations of a String The Wave Equation Eigenvalues and Eigenfunctions Linear Operators and Manifolds Invariant Manifolds Physical Quantities as Operators Harmonic Oscillator Eigenfunctions of Hydrogen-like Atoms The Rigid RotatorVII. Vibrations of a Dynamical System Kinetic and Potential Energies of a Dynamical System Lagrangian Equations of Motion Normal Modes of Oscillation Normal Frequencies Orthogonality Relation between the Normal Co-ordinates Symmetry Properties of Normal Modes Representation Defined by the Cartesian Co-ordinates Determination of the Normal Co-ordinates Splitting of the Secular Equation F and G MatricesVIII. Vibrational Raman Effect and Infra-Red Absorption The Molecule as a Dynamical System Raman Scattering by a Diatomic Molecule Infra-Red Absorption and Electric Moment Selection Rules for Fundamentals Overtone and Combination Lines Selection Rules in Some Special CasesIX. Molecular Structure and Normal Modes Triatomic Molecules. Pyramidal Molecules The Nitrate and the Carbonate Ions Diatomic and Other Linear Molecules SulfurX. Molecular Structure and Normal Frequencies Interatomic Forces Water PhosphorusXI. Lattices in Three Dimensions Space Lattices Crystal Classes Space GroupsXII. Raman and Infra-Red Spectra of Crystals The Internal Structure of a Crystal Application of Group Theory Lattice Oscillations in Calcite and Sodium Nitrate Some Special Cases Lattice Oscillations in Some Organic Crystals Raman Spectra and Different Crystalline Modifications Splitting of Degenerate Modes in Crystals of Lower Symmetry Special Case of DiamondXIII. Crystal Symmetry and Physical Properties General Considerations Crystal Optics Elasticity and Photoelasticity Description of the General Method Results Enantiomorphism and Optical Activity Isotropic SolidsXIV. Rotation Groups The Rotation Groups in Two and Three Dimensions Unitary Substitutions of Two Variables Irreducible Manifolds with Respect to U2 Irreducible Representations of U2 Characters of the Group U2 The Irreducible Components of iD X λD Isomorphism between the Rotation and the Unitary GroupsXV. Application to Problems of Atomic Spectra Solutions of the Wave Equation Angular Momentum Operators Quantization of Angular Momentum and Its Components Vector Addition of Angular Momenta Reduction of the Product Manifold Selection Rules and Intensities of Spectral Lines Pauli Theory Pauli Exclusion PrincipleXVI. Other Applications The Hydrogen Molecule Rotational Specific Heat of Hydrogen Nuclear Spin Intensities of Rotational Raman LinesAppendices I. Representations of Finite Groups II. Transformation of Matrices III. Kramers-Heisenberg Dispersion Formula IV. Evaluation of Group Characters V. Properties of Some Polynomial Functions VI. Laplacian Operator VII. Parameter Groups VIII. Character Tables and Irreducible Representations in Respect of Various Point GroupsIndex