Primer for Point and Space Groups (Undergraduate Texts in Contemporary Physics) (2004. XIII, 220 p. w. 39 figs. 24,5 cm)

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Primer for Point and Space Groups (Undergraduate Texts in Contemporary Physics) (2004. XIII, 220 p. w. 39 figs. 24,5 cm)

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  • 製本 Hardcover:ハードカバー版/ページ数 220 p.
  • 商品コード 9780387402482

基本説明

Written in the spirit of Liboff's acclaimed text on Quantum Mechanics, this introduction to offers an exceptionally clear presentation with a good sense of what to explain.

Table of Contents

Preface                                            vii
1 Groups and Subgroups 1 (17)
1.1 Definitions and Basics 1 (2)
1.2 Group Table 3 (1)
1.3 Rearrangement Theorem 4 (3)
1.4 Building Groups. Subgroups 7 (7)
Summary of Topics for Chapter 1 14 (1)
Problems 15 (3)
2 Classes and Platonic Solids 18 (18)
2.1 Conjugate Elements 18 (1)
2.2 Classes 19 (1)
2.3 Direct Product 20 (1)
2.4 Cnv and Dn Groups 20 (5)
2.5 Platonic Solids. T, O and I Groups 25 (7)
Summary of Topics for Chapter 2 32 (1)
Problems 33 (3)
3 Matrices, Irreps and the Great Orthogonality 36 (18)
Theorem
3.1 Matrix Representations of Operators 36 (5)
3.2 Irreducible Representations 41 (1)
3.3 Great Orthogonality Theorem (GOT) 42 (2)
3.4 Six Important Rules 44 (2)
3.5 Character Tables. Bases 46 (2)
3.6 Representations of Cyclic Groups 48 (3)
Summary of Topics for Chapter 3 51 (1)
Problems 52 (2)
4 Quantum Mechanics, the Full Rotation Group, 54 (35)
and Young Diagrams
4.1 Application to Quantum Mechanics 54 (4)
4.2 Full Rotation Group O(3) 58 (2)
4.3 SU(2) 60 (5)
4.4 Irreps of O(3)+ and Coupled Angular 65 (3)
Momentum States
4.5 Symmetric Group; Cayley's Theorem 68 (5)
4.6 Young Diagrams 73 (7)
4.7 Degenerate Perturbation Theory 80 (3)
Summary of Topics for Chapter 4 83 (1)
Problems 84 (5)
5 Space Groups, Brillouin Zone and the Group of 89 (47)
k
5.1 Cosets and Invariant Subgroups. The 89 (3)
Factor Group
5.2 Primitive Vectors. Braviais Lattice. 92 (4)
Reciprocal Lattice Space
5.3 Crystallographic Point Groups and 96 (7)
Reciprocal Lattice Space
5.4 Bloch Waves and Space Groups 103(17)
5.5 Application to Semiconductor Materials 120 (4)
5.6 Time Reversal, Space Inversion and Double 124(6)
Space Groups
Summary of Topics for Chapter 5 130(1)
Problems 131(5)
6 Atoms in Crystals and Correlation Diagrams 136 (24)
6.1 Central-Field Approximation 136(2)
6.2 Atoms in Crystal Fields 138(4)
6.3 Correlation Diagrams 142(2)
6.4 Electric and Magnetic Material Properties 144(11)
6.5 Tensors in Group Theory 155(3)
Summary of Topics for Chapter 6 158(1)
Problems 159(1)
7 Elements of Abstract Algebra and the Galois 160 (34)
Group
7.1 Integral Domains, Rings and Fields 160(5)
7.2 Numbers 165(6)
7.3 Irreducible Polynomials 171(7)
7.4 The Galois Group 178(9)
Symbols for Chapter 7 187(1)
Summary of Topics for Chapter 7 188(1)
Problems 189(5)
Appendix A: Character Tables for the Point 194(18)
Groups
Appendix B: Irreps for the Oh and Doh Groups, 212(1)
their Dimensions and Notations
Bibliography of Works in Group Theory and 213 (4)
Allied Topics
Index 217