Group Theory and Its Applications in Physics - Softcover

Inhaltsangabe

1. Symmetry and the Role of Group Theory.- 1.1 Arrangement of the Book.- 2. Groups.- 2.1 Definition of a Group.- 2.1.1 Multiplication Tables.- 2.1.2 Generating Elements.- 2.1.3 Commutative Groups.- 2.2 Covering Operations of Regular Polygons.- 2.3 Permutations and the Symmetric Group.- 2.4 The Rearrangement Theorem.- 2.5 Isomorphism and Homomorphism.- 2.5.1 Isomorphism.- 2.5.2 Homomorphism.- 2.5.3 Note on Mapping.- 2.6 Subgroups.- 2.7 Cosets and Coset Decomposition.- 2.8 Conjugate Elements; Classes.- 2.9 Multiplication of Classes.- 2.10 Invariant Subgroups.- 2.11 The Factor Group.- 2.11.1 The Kernel.- 2.11.2 Homomorphism Theorem.- 2.12 The Direct-Product Group.- 3. Vector Spaces.- 3.1 Vectors and Vector Spaces.- 3.1.1 Mathematical Definition of a Vector Space.- 3.1.2 Basis of a Vector Space.- 3.2 Transformation of Vectors.- 3.3 Subspaces and Invariant Subspaces.- 3.4 Metric Vector Spaces.- 3.4.1 Inner Product of Vectors.- 3.4.2 Orthonormal Basis.- 3.4.3 Unitary Operators and Unitary Matrices.- 3.4.4 Hermitian Operators and Hermitian Matrices.- 3.5 Eigenvalue Problems of Hermitian and Unitary Operators.- 3.6 Linear Transformation Groups.- 4. Representations of a Group I.- 4.1 Representations.- 4.1.1 Basis for a Representation.- 4.1.2 Equivalence of Representations.- 4.1.3 Reducible and Irreducible Representations.- 4.2 Irreducible Representations of the Group C?v.- 4.3 Effect of Symmetry Transformation Operators on Functions.- 4.4 Representations of the Group C3v Based on Homogeneous Polynomials.- 4.5 General Representation Theory.- 4.5.1 Unitarization of a Representation.- 4.5.2 Schur's First Lemma.- 4.5.3 Schur's Second Lemma.- 4.5.4 The Great Orthogonality Theorem T.- 4.6 Characters.- 4.6.1 First and Second Orthogonalities of Characters.- 4.7 Reduction of Reducible Representations.- 4.7.1 Restriction to a Subgroup.- 4.8 Product Representations.- 4.8.1 Symmetric and Antisymmetric Product Representations.- 4.9 Representations of a Direct-Product Group.- 4.10 The Regular Representation.- 4.11 Construction of Character Tables.- 4.12 Adjoint Representations.- 4.13 Proofs of the Theorems on Group Representations.- 4.13.1 Unitarization of a Representation.- 4.13.2 Schur's First Lemma.- 4.13.3 Schur's Second Lemma.- 4.13.4 Second Orthogonality of Characters.- 5. Representations of a Group II.- 5.1 Induced Representations.- 5.2 Irreducible Representations of a Group with an Invariant Subgroup.- 5.3 Irreducible Representations of Little Groups or Small Representations.- 5.4 Ray Representations.- 5.5 Construction of Matrices of Irreducible Ray Representations.- 6. Group Representations in Quantum Mechanics.- 6.1 Symmetry Transformations of Wavefunctions and Quantum-Mechanical Operators.- 6.2 Eigenstates of the Hamiltonian and Irreducibility.- 6.3 Splitting of Energy Levels by a Perturbation.- 6.4 Orthogonality of Basis Functions.- 6.5 Selection Rules.- 6.5.1 Derivation of the Selection Rule for Diagonal Matrix Elements.- 6.6 Projection Operators.- 7. The Rotation Group.- 7.1 Rotations.- 7.2 Rotation and Euler Angles.- 7.3 Rotations as Operators; Infinitesimal Rotations.- 7.4 Representation of Infinitesimal Rotations.- 7.4.1 Rotation of Spin Functions.- 7.5 Representations of the Rotation Group.- 7.6 SU(2), SO(3) and O(3).- 7.7 Basis of Representations.- 7.8 Spherical Harmonics.- 7.9 Orthogonality of Representation Matrices and Characters.- 7.9.1 Completeness Relation for XJ(?).- 7.10 Wigner Coefficients.- 7.11 Tensor Operators.- 7.12 Operator Equivalents.- 7.13 Addition of Three Angular Momenta;Racah Coefficients.- 7.14 Electronic Wavefunctions for the Configuration (nl)x.- 7.15 Electrons and Holes.- 7.16 Evaluation of the Matrix Elements of Operators.- 8. Point Groups.- 8.1 Symmetry Operations in Point Groups.- 8.2 Point Groups and Their Notation.- 8.3 Class Structure in Point Groups.- 8.4 Irreducible Representations of Point Groups.- 8.5 Double-Valued Representations and Double Groups.- 8.6 Transformation of Spin and Orbital Func

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