Part I Basic Mathematics 1 Basic Mathematical Background: Introduction 1.1 Definition of a Group 1.2 Simple Example of a Group 1.3 Basic Definitions 1.4 Rearrangement Theorem 1.5 Cosets 1.6 Conjugation and Class 1.7 Factor Groups 1.8 Group Theory and Quantum Mechanics 2 Representation Theory and Basic Theorems 2.1 Important Definitions 2.2 Matrices 2.3 Irreducible Representations 2.4 The Unitarity of Representations 2.5 Schur's Lemma (Part 1) 2.6 Schur's Lemma (Part 2) 2.7 Wonderful Orthogonality Theorem 2.8 Representations and Vector Spaces 3 Character of a Representation 3.1 Definition of Character 3.2 Characters and Class 3.3 Wonderful Orthogonality Theorem for Character 3.4 Reducible Representations 3.5 The Number of Irreducible Representations 3.6 Second Orthogonality Relation for Characters 3.7 Regular Representation 3.8 Setting up Character Tables …… 4 Basis Functions Part II Introductory Application to Quantum Systems 5 Splitting of Atomic Orbitals in a Crystal Potential 6 Application to Selection Rules and Direct Products Part III Molecular Systems 7 Electronic States of Molecules and Directed Valence 8 Molecular Vibrations, Infrared, and Raman Activity Part IV Application to Periodic Lattices 9 Space Groups in Real Space 10 Space Groups in Reciprocal Space and Representations Part V Electron and Phonon Dispersion Relation 11 Applications to Lattice Vibrations 12 Electronic Energy Levels in a Cubic Crystals 13 Energy Band Models Based on Symmetry 14 Spin–Orbit Interaction in Solids and Double Groups 15 Application of Double Groups to Energy Bands with Spin Part VI Other Symmetries 16 Time Reversal Symmetry 17 Permutation Groups and Many-Electron States 18 Symmetry Properties of Tensors A Point Group Character Tables
B Two-Dimensional Space Groups C Tables for 3D Space Groups D Tables for Double Groups E Group Theory Aspects of Carbon Nanotubes F Permutation Group Character Tables References Index
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