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Symmetry and Condensed Matter Physics A Computational Approach

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ISBN-10: 0521828457

ISBN-13: 9780521828451

Edition: 2008

Authors: M. El-Batanouny, F. Wooten

List price: $160.00
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The first attempt to fuse symmetry, condensed matter and computational methods into one pedagogical textbook, this textbook includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; and concepts and techniques behind the Landau theory of phase transitions. The textbook adopts and develops a computational approach to the application of group theoretical techniques to solving symmetry related problems. This dramatically alleviates the need for intensive calculations, even for the simplest systems, usually found in the…    
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Book details

List price: $160.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 3/13/2008
Binding: Hardcover
Pages: 936
Size: 7.00" wide x 10.00" long x 2.00" tall
Weight: 4.290
Language: English

Frederick Wooten (1928-2004) was Professor of Physics and Chair of the Department of Applied Science at the University of California, Davis. He is the author of Optical Properties of Solids, and numerous articles in the field of solid state physics, more recently in the area of materials science.

Symmetry and physics
Hamiltonians, eigenfunctions, and eigenvalues
Symmetry operators and operator algebra
Point-symmetry operations
Applications to quantum mechanics
Symmetry and group theory
Groups and their realizations
The symmetric group
Computational aspects
Homomorphism, isomorphism, and automorphism
Direct- or outer-product groups
Group representations: concepts
Representations and realizations
Generation of representations on a set of basis functions
Group representations: formalism and methodology
Matrix representations
Character of a matrix representation
Burnside's method
Computational projects
Dixon's method for computing group characters
The eigenvalue equation modulo p
Dixon's method for irreducible characters
Computer codes for Dixon's method
Finding eigenvalues and eigenvectors
Appendix 2
Computation project
Group action and symmetry projection operators
Group action
Symmetry projection operators
The regular projection matrices: the simple characteristic
Construction of the irreducible representations
Eigenvectors of the regular Rep
The symmetry structure of the regular Rep eigenvectors
Symmetry projection on regular Rep eigenvectors
Computer construction of Irreps with d[subscript alpha] > 1
Summary of the method
Product groups and product representations
Subgroups and cosets
Direct outer-product groups
Semidirect product groups
Direct inner-product groups and their representations
Product representations and the Clebsch-Gordan series
Computer codes
Induced representations
Subduced Reps and compatibility relations
Induction of group Reps from the Irreps of its subgroups
Irreps induced from invariant subgroups
Examples of Irrep induction using the method of little-groups
Frobenius reciprocity theorem and other useful theorems
Crystallographic symmetry and space-groups
Euclidean space
The perfect crystal
Space-group operations: the Seitz operators
Symmorphic and nonsymmorphic space-groups
Site-symmetries and the Wyckoff notation
Fourier space crystallography
Space-groups: Irreps
Irreps of the translation group
Induction of Irreps of space-groups
Time-reversal symmetry: color groups and the Onsager relations
The time-reversal operator in quantum mechanics
Spin-1/2 and double-groups
Magnetic and color groups
The time-reversed representation: theory of corepresentations
Theory of crystal fields
Onsager reciprocity theorem (Onsager relations) and transport properties
Tensors and tensor fields
Tensors and their space-time symmetries
Construction of symmetry-adapted tensors
Description and classification of matter tensors
Tensor field representations
Electronic properties of solids
The one-electron approximations and self-consistent-field theories
Methods and techniques for band structure calculations
Electronic structure of magnetically ordered systems
Derivation of the Hartree-Fock equations
Holstein-Primakoff (HP) operators
Dynamical properties of molecules, solids, and surfaces
Dynamical properties of molecules
Dynamical properties of solids
Dynamical properties of surfaces
Coulomb interactions and the method of Ewald summations
Electronic effects on phonons in insulators and semiconductors
Experimental measurements and selection rules
Selection rules
Differential scattering cross-sections in the Born approximation
Light scattering spectroscopies
Photoemission and dipole selection rules
Neutron and atom scattering spectroscopies
Landau's theory of phase transitions
Phase transitions and their classification
Landau theory of phase transitions: principles
Construction and minimization techniques for [Delta phi]
Incommensurate systems and quasi-crystals
The concept of higher-dimensional spaces: superspaces and superlattices
Quasi-crystal symmetry: the notion of indistinguishability and the classification of space-groups
Two-dimensional lattices, cyclotomic integers, and axial stacking