Group Theory in Solid State Physics and Photonics : Problem Solving with Mathematica

種類:

電子ブック

責任表示:

Wolfram Hergert and R. Matthias Geilhufe

出版情報:

2018

著者名:

• Hergert, W.
• Geilhufe, R. Matthias

ISBN:

9783527413003 [3527413006]    
9783527695799 [3527695796]    
9783527413010 [3527413014]    
9783527413027 [3527413022]    

注記:

Online resource; title from PDF title page (EBSCO, viewed April 26, 2018).
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
While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic ap

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