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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version : |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
W Hergert; R Matthias Geilhufe |

ISBN: | 9783527413003 3527413006 9783527695799 3527695796 9783527413010 3527413014 9783527413027 3527413022 |

OCLC Number: | 1032303077 |

Description: | 1 online resource |

Contents: | Cover; Main title; Copyright page; Contents; Preface; 1 Introduction; 1.1 Symmetries in Solid-State Physics and Photonics; 1.2 A Basic Example: Symmetries of a Square; Part One Basics of Group Theory; 2 Symmetry Operations and Transformations of Fields; 2.1 Rotations and Translations; 2.1.1 Rotation Matrices; 2.1.2 Euler Angles; 2.1.3 Euler-Rodrigues Parameters and Quaternions; 2.1.4 Translations and General Transformations; 2.2 Transformation of Fields; 2.2.1 Transformation of Scalar Fields and Angular Momentum; 2.2.2 Transformation of Vector Fields and Total Angular Momentum; 2.2.3 Spinors. 3 Basics Abstract Group Theory3.1 Basic Definitions; 3.1.1 Isomorphism and Homomorphism; 3.2 Structure of Groups; 3.2.1 Classes; 3.2.2 Cosets and Normal Divisors; 3.3 Quotient Groups; 3.4 Product Groups; 4 Discrete Symmetry Groups in Solid-State Physics and Photonics; 4.1 Point Groups; 4.1.1 Notation of Symmetry Elements; 4.1.2 Classification of Point Groups; 4.2 Space Groups; 4.2.1 Lattices, Translation Group; 4.2.2 Symmorphic and Nonsymmorphic Space Groups; 4.2.3 Site Symmetry, Wyckoff Positions, and Wigner-Seitz Cell; 4.3 Color Groups and Magnetic Groups; 4.3.1 Magnetic Point Groups. 4.3.2 Magnetic Lattices4.3.3 Magnetic Space Groups; 4.4 Noncrystallographic Groups, Buckyballs, and Nanotubes; 4.4.1 Structure and Group Theory of Nanotubes; 4.4.2 Buckminsterfullerene C60; 5 Representation Theory; 5.1 Definition of Matrix Representations; 5.2 Reducible and Irreducible Representations; 5.2.1 The Orthogonality Theorem for Irreducible Representations; 5.3 Characters and Character Tables; 5.3.1 The Orthogonality Theorem for Characters; 5.3.2 Character Tables; 5.3.3 Notations of Irreducible Representations; 5.3.4 Decomposition of Reducible Representations. 5.4 Projection Operators and Basis Functions of Representations5.5 Direct Product Representations; 5.6 Wigner-Eckart Theorem; 5.7 Induced Representations; 6 Symmetry and Representation Theory in k-Space; 6.1 The Cyclic Born-von Kármán Boundary Condition and the Bloch Wave; 6.2 The Reciprocal Lattice; 6.3 The Brillouin Zone and the Group of the Wave Vector k; 6.4 Irreducible Representations of Symmorphic Space Groups; 6.5 Irreducible Representations of Nonsymmorphic Space Groups; Part Two Applications in Electronic Structure Theory; 7 Solution of the Schrödinger Equation. 7.1 The Schrödinger Equation7.2 The Group of the Schrödinger Equation; 7.3 Degeneracy of Energy States; 7.4 Time-Independent Perturbation Theory; 7.4.1 General Formalism; 7.4.2 Crystal Field Expansion; 7.4.3 Crystal Field Operators; 7.5 Transition Probabilities and Selection Rules; 8 Generalization to Include the Spin; 8.1 The Pauli Equation; 8.2 Homomorphism between SU(2) and SO(3); 8.3 Transformation of the Spin-Orbit Coupling Operator; 8.4 The Group of the Pauli Equation and Double Groups; 8.5 Irreducible Representations of Double Groups. |

Responsibility: | Wolfram Hergert and R. Matthias Geilhufe. |

### Abstract:

While group theory is well established, this textbook raises two completely new aspects: gaining a better understanding by focusing on problem solving, making extensive use of Mathematica; offering a new tool for photonics by applying the concepts to photonic fibers and crystals.
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