Primer for Point and Space Groups [E-Book] / by Richard L. Liboff.
This text stems from a course I have taught a number of times, attended by students of material science, electrical engineering, physics, chemistry, physical chemistry and applied mathematics. It is intended as an intro ductory discourse to give the reader a first encounter with group theory. The w...
Saved in:
Full text |
|
Personal Name(s): | Liboff, Richard L., author |
Imprint: |
New York, NY :
Springer,
2004
|
Physical Description: |
XIV, 220 p. online resource. |
Note: |
englisch |
ISBN: |
9781468493832 |
DOI: |
10.1007/978-1-4684-9383-2 |
Series Title: |
/* Depending on the record driver, $field may either be an array with
"name" and "number" keys or a flat string containing only the series
name. We should account for both cases to maximize compatibility. */?>
Undergraduate Texts in Contemporary Physics
|
Subject (LOC): |
- 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.