5.6 Small Representations of the Group of the Wavevector -- 5.7 Irreducible Representations of Space Groups -- 5.8 Compatibility Relations -- References -- 6 Tables -- 6.1 Summary of Theory and Guide to Tables -- 6.1.1 Summary of Theory -- 6.1.2 Guide to Tables -- 6.2 Elements and Multiplication Tables of the Groups Oh and D6h -- 6.3 Groups C2, Ci and Cs -- 6.4 Group C3 -- 6.5 Groups C4 and S4 -- 6.6 Groups D2, C2h and C2v -- 6.7 Groups C6, S6 and C3h -- 6.8 Groups D3 and C3v -- 6.9 Groups D4, C4v and D2d -- 6.10 Group C4h -- 6.11 Group D2h -- 6.12 Groups D6, D3d, C6v and D3h -- 6.13 Group T -- 6.14 Group C6h -- 6.15 Group D4h -- 6.16 Groups O and Td -- 6.17 Group D6h -- 6.18 Group Th -- 6.19 Group Oh -- 6.20 Example of the Use of the Tables: The Space Group Oh7 -- References -- 7 Group Theory and Quantum Mechanics -- 7.1 Representation Spaces -- 7.1.1 Basis Functions -- 7.1.2 Expansion Theorem -- 7.1.3 Reduction by Idempotent Operators -- 7.1.4 Orthogonality of the Basis Functions -- 7.1.5 Criterion for Representation Functions -- 7.2 Classification of States -- 7.2.1 Hamiltonian of a System with Symmetry -- 7.2.2 Eigenspaces and Representations -- 7.3 Splitting of Eigenvalues -- 7.3.1 Schrödinger Perturbation Theory -- 7.3.2 Effect of Symmetry -- 7.4 Selection Rules -- References -- 8 Group Theory and Solid-State Physics -- 8.1 Electron in a Periodic Field -- 8.1.1 Mathematical Formulation of the Problem -- 8.1.2 The Ritz Method -- 8.2 Symmetrized Coordinate Functions -- 8.2.1 Construction of Symmetrized Functions -- 8.2.2 Matrix Elements of the Hamiltonian -- 8.3 Double-Valued Representations -- 8.4 Time-Reversal Symmetry -- 8.4.1 Time-Reversal Operator -- 8.4.2 Systems with Time-Reversal Symmetry -- 8.4.3 Criterion of Extra Degeneracy -- References -- 9 Energy Band Calculation -- 9.1 Basics of Band Calculations -- 9.2 The OPW Method. |