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5.1 How to Manage Quantum-Dynamics in Crystal?5.2 Control of Band Gaps by Means of the Wyckoff Positions; 5.3 A Possible Plan of Material Design in the Super-Cell; References; 6 Technical Details; 6.1 About This Chapter; 6.2 Determination of Crystal Symmetry; 6.3 Symmetry Operations in the Reciprocal Space; 6.4 The Computation of the Compatibility Relation; 6.5 The Character Table at the Boundary of the Brillouin Zone; 6.5.1 The Necessity of the Special Treatment for the Non-symmorphic Crystal; 6.5.2 Herring Method: An Example; 6.6 The Semidirect Product and the Induced Representation
6.7 The Computation of the Character Table in the Cubic Diamond by GAP6.8 Crystal Lattice and Cohomology; 6.8.1 A Brief Introduction to Group Cohomology; 6.8.2 The Possible Fractional Translations with One Point Group; 6.8.3 Group Extension; 6.9 Remarks to This Chapter; References; 7 Symmetry in C60; 7.1 The Initial Set-Up; 7.2 The Analysis of the Eigenstates; 7.3 The Analysis Again, Against the Failure in the Identification; 7.4 The Perturbation and the Symmetry; 7.5 The Possible Deformation in the Reduced Symmetry
7.6 The Reduction of the Symmetry, from the View Point of the Orbit in the Permutation7.7 The Symmetry in the Eigenstates (Hidden One); 7.8 The Super-Symmetries; 7.9 Remarks to This Chapter; Reference; 8 Analysis of Vibrational Mode in C60; 8.1 The Vibrational Modes of C60; 8.2 One Technical Problem; 8.3 Remark to This Chapter; References; 9 Final Remarks; References; A Symmetry Operations in the Diamond Structure (Real Space); Appendix B Symmetry Operations in the Hexagonal Lattice (Real Space); Appendix C Symmetry Operations in the Diamond Structure (Wave-Number Space)
Appendix D Symmetry Operations in the Hexagonal Lattice (Wave-Number Space)Appendix E The Computation of Wyckoff Positions by GAP; Appendix F Subgroup Lattice; Appendix G A Short Program to Compute the Semidirect Product of Groups; Appendix H The Analytical Representation of the Energy Spectra of C60; Appendix I Comment on the Irreducible Representations in the Symmetry Group of C60; Appendix J The GAP Script in the Computation of Deformation in C60
6.7 The Computation of the Character Table in the Cubic Diamond by GAP6.8 Crystal Lattice and Cohomology; 6.8.1 A Brief Introduction to Group Cohomology; 6.8.2 The Possible Fractional Translations with One Point Group; 6.8.3 Group Extension; 6.9 Remarks to This Chapter; References; 7 Symmetry in C60; 7.1 The Initial Set-Up; 7.2 The Analysis of the Eigenstates; 7.3 The Analysis Again, Against the Failure in the Identification; 7.4 The Perturbation and the Symmetry; 7.5 The Possible Deformation in the Reduced Symmetry
7.6 The Reduction of the Symmetry, from the View Point of the Orbit in the Permutation7.7 The Symmetry in the Eigenstates (Hidden One); 7.8 The Super-Symmetries; 7.9 Remarks to This Chapter; Reference; 8 Analysis of Vibrational Mode in C60; 8.1 The Vibrational Modes of C60; 8.2 One Technical Problem; 8.3 Remark to This Chapter; References; 9 Final Remarks; References; A Symmetry Operations in the Diamond Structure (Real Space); Appendix B Symmetry Operations in the Hexagonal Lattice (Real Space); Appendix C Symmetry Operations in the Diamond Structure (Wave-Number Space)
Appendix D Symmetry Operations in the Hexagonal Lattice (Wave-Number Space)Appendix E The Computation of Wyckoff Positions by GAP; Appendix F Subgroup Lattice; Appendix G A Short Program to Compute the Semidirect Product of Groups; Appendix H The Analytical Representation of the Energy Spectra of C60; Appendix I Comment on the Irreducible Representations in the Symmetry Group of C60; Appendix J The GAP Script in the Computation of Deformation in C60