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Group theory in solid state physics and photonics : problem solving with Mathematica / Wolfram Hergert and R. Matthias Geilhufe

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Publisher: Weinheim : Wiley-VCH, [2018]Copyright date: © 2018Description: 1 Online-RessourceISBN:
  • 9783527413003
  • 9783527413010
  • 9783527413027
  • 9783527695799
Subject(s): Additional physical formats: 9783527411337 | Erscheint auch als: Group theory in solid state physics and photonics. Druck-Ausgabe Weinheim, Germany : Wiley-VCH Verlag GmbH & Co. KGaA, 2018. XIII, 364 SeitenDDC classification:
  • 530.41
MSC: MSC: *82-02 | 82D20 | 82D25 | 20H15 | 68N15 | 00A79RVK: RVK: UP 1200LOC classification:
  • QC176
Online resources: Summary: 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 GroupsSummary: 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 RepresentationsSummary: 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 EquationSummary: 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 GroupsSummary: 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 SpinorsPPN: PPN: 1026366151Package identifier: Produktsigel: ZDB-4-NLEBK
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