Primer for Point and Space Groups / Edition 1by Richard Liboff
Pub. Date: 12/18/2003
Publisher: Springer New York
Written in the spirit of Liboff's acclaimed text on Quantum Mechanics, this introduction to group theory offers an exceptionally clear presentation with a good sense of what to explain, which examples are most appropriate, and when to give a counter-example. Group Theory Primer is an ideal introductory text for undergraduates in physics, engineering, materials
Written in the spirit of Liboff's acclaimed text on Quantum Mechanics, this introduction to group theory offers an exceptionally clear presentation with a good sense of what to explain, which examples are most appropriate, and when to give a counter-example. Group Theory Primer is an ideal introductory text for undergraduates in physics, engineering, materials science, and chemistry. It should also provide a good background for those students who go on to use group theory in such applications as nuclear and particle physics. Liboff covers the standard topics, but in a way that allows students to see the physical implications of the defined concept. Among the many introductions to group theory pitched at the undergraduate level, few can match this text for the logic and lucidity of its presentation.
- Springer New York
- Publication date:
- Undergraduate Texts in Contemporary Physics Series
- Edition description:
- Product dimensions:
- 9.21(w) x 6.14(h) x 0.56(d)
Table of Contents
1 Groups and Subgroups.- 1.1 Definitions and Basics.- 1.2 Group Table.- 1.3 Rearrangement Theorem.- 1.4 Building Groups. Subgroups.- Summary of Topics for Chapter 1.- Problems.- 2 Classes and Platonic Solids.- 2.1 Conjugate Elements.- 2.2 Classes.- 2.3 Direct Product.- 2.4 Cnv and Dn Groups.- 2.5 Platonic Solids. T, O and I Groups.- Summary of Topics for Chapter 2.- Problems.- 3 Matrices, Irreps and the Great Orthogonality Theorem.- 3.1 Matrix Representations of Operators.- 3.2 Irreducible Representations.- 3.3 Great Orthogonality Theorem (GOT).- 3.4 Six Important Rules.- 3.5 Character Tables. Bases.- 3.6 Representations of Cyclic Groups.- Summary of Topics for Chapter 3.- Problems.- 4 Quantum Mechanics, the Full Rotation Group, and Young Diagrams.- 4.1 Application to Quantum Mechanics.- 4.2 Full Rotation Group O(3).- 4.3 SU(2).- 4.4 Irreps of O(3)+ and Coupled Angular Momentum States.- 4.5 Symmetric Group; Cayley’s Theorem.- 4.6 Young Diagrams.- 4.7 Degenerate Perturbation Theory.- Summary of Topics for Chapter 4.- Problems.- 5 Space Groups, Brillouin Zone and the Group of k.- 5.1 Cosets and Invariant Subgroups. The Factor Group.- 5.2 Primitive Vectors. Braviais Lattice. Reciprocal Lattice Space.- 5.3 Crystallographic Point Groups and Reciprocal Lattice Space.- 5.4 Bloch Waves and Space Groups.- 5.5 Application to Semiconductor Materials.- 5.6 Time Reversal, Space Inversion and Double Space Groups.- Summary of Topics for Chapter 5.- Problems.- 6 Atoms in Crystals and Correlation Diagrams.- 6.1 Central-Field Approximation.- 6.2 Atoms in Crystal Fields.- 6.3 Correlation Diagrams.- 6.4 Electric and Magnetic Material Properties.- 6.5 Tensors in Group Theory.- Summary of Topics for Chapter 6.- Problems.- 7 Elements of Abstract Algebra and the Galois Group.- 7.1 Integral Domains, Rings and Fields.- 7.2 Numbers.- 7.3 Irreducible Polynomials.- 7.4 The Galois Group.- Symbols for Chapter 7.- Summary of Topics for Chapter 7.- Problems.- Appendix A: Character Tables for the Point Groups.- Bibliography of Works in Group Theory and Allied Topics.
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