The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space GroupsOxford University Press, 10. 12. 2009 - Počet stran: 768 This book gives the complete theory of the irreducible representations of the crystallographic point groups and space groups. This is important in the quantum-mechanical study of a particle or quasi-particle in a molecule or crystalline solid because the eigenvalues and eigenfunctions of a system belong to the irreducible representations of the group of symmetry operations of that system. The theory is applied to give complete tables of these representations for all the 32 point groups and 230 space groups, including the double-valued representations. For the space groups, the group of the symmetry operations of the k vector and its irreducible representations are given for all the special points of symmetry, lines of symmetry and planes of symmetry in the Brillouin zone. Applications occur in the electronic band structure, phonon dispersion relations and selection rules for particle-quasiparticle interactions in solids. The theory is extended to the corepresentations of the Shubnikov (black and white) point groups and space groups. |
Obsah
1 | |
2 SYMMETRYADAPTED FUNCTIONS FOR THE POINT GROUPS | 51 |
3 SPACE GROUPS | 81 |
4 THE REPRESENTATIONS OF A GROUP IN TERMS OF THE REPRESENTATIONS OF AN INVARIANT SUBGROUP | 171 |
5 THE SINGLEVALUED REPRESENTATIONS OF THE 230 SPACE GROUPS | 225 |
6 THE DOUBLEVALUED REPRESENTATIONS OF THE 32 POINT GROUPS AND THE 230 SPACE GROUPS | 418 |
7 THE MAGNETIC GROUPS AND THEIR COREPRESENTATIONS | 569 |
APPENDIX | 682 |
684 | |
737 | |
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The Mathematical Theory of Symmetry in Solids: Representation Theory for ... Christopher Bradley,Arthur Cracknell Náhled není k dispozici. - 2010 |
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A₁ B₁ B₂ Bravais lattice Brillouin zone C₁ C₁ C₂ C3 C₁₁ C₁₂ C₂ C₂x C₂z character table corepresentations coreps crystal crystallographic point groups cubic E₁ elements English Transl example functions G₁ G₁₂ G₂ given group G GT₂ invariant subgroup irreducible representations k₁ Kronecker products labels little co-group little group magnetic matrix notation Orthorhombic P²Q P²QR P²R P³Q P³QR P³R point groups points of symmetry projective representations R₁ R₂ reps of G rotation small reps Soviet Phys space groups space-group reps t₁ or t₂ t₂ or t3 Theorem theory time-reversal symmetry tỷ unit cell unitary wave vector α α α ΓΑ Γι σ₂ ΣΧ