Amazon cover image
Image from Amazon.com

Symmetry and Condensed Matter Physics : A Computational Approach.

By: Contributor(s): Publisher: Cambridge : Cambridge University Press, 2008Copyright date: ©2008Description: 1 online resource (938 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511392085
Subject(s): Genre/Form: Additional physical formats: Print version:: Symmetry and Condensed Matter Physics : A Computational ApproachDDC classification:
  • 530.41
LOC classification:
  • QC174.17.S9 -- E43 2008eb
Online resources:
Contents:
Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Symmetry and physics -- 1.1 Introduction -- 1.2 Hamiltonians, eigenfunctions, and eigenvalues -- 1.2.1 Examples of symmetry and conservation laws -- Translation and conservation of linear momentum -- Inversion and parity conservation -- 1.3 Symmetry operators and operator algebra -- 1.3.1 Configuration-space operators -- 1.3.2 Function-space operations -- 1.3.3 Operator algebra -- 1.4 Point-symmetry operations -- 1.5 Applications to quantum mechanics -- Exercises -- 2 Symmetry and group theory -- 2.1 Groups and their realizations -- 2.2 The symmetric group -- 2.2.1 The permutation group -- 2.3 Computational aspects -- 2.3.1 Generation of the Cayley (multiplication) table -- Rank, basis and presentation of a group -- 2.3.2 Computer generation of group elements -- 2.4 Classes -- Geometric interpretation -- 2.4.1 Computer generation of classes and class arrays -- 2.4.2 Class multiplication -- Class rearrangement theorem -- A conjugation operation simply rearranges the list of distinct elements of a class. -- 2.4.3 Computer generation of class multiplication matrices -- 2.5 Homomorphism, isomorphism, and automorphism -- 2.6 Direct- or outer-product groups -- Exercises -- 3 Group representations: concepts -- 3.1 Representations and realizations -- 3.1.1 Transformation of coordinates -- 3.1.2 Transformation of functions -- 3.2 Generation of representations on a set of basis functions -- Exercises -- 4 Group representations: formalism and methodology -- 4.1 Matrix representations -- 4.1.1 Diagonal matrix representatives -- 4.1.2 Reducible representations -- 4.1.3 The regular representation -- 4.1.4 The great orthogonality theorem -- 4.2 Character of a matrix representation -- 4.2.1 Character orthogonality relations -- 4.2.2 Character decomposition.
4.2.3 Class matrices and Dirac characters -- 4.3 Burnside's method -- Exercises -- Computational projects -- 5 Dixon's method for computing group characters -- 5.1 The eigenvalue equation modulo p -- 5.2 Dixon's method for irreducible characters -- 5.2.1 Integer polynomials modulo p -- 5.2.2 Multiplicities and the character -- 5.3 Computer codes for Dixon's method -- Appendix 1 Finding eigenvalues and eigenvectors -- The Gauss elimination method: a peculiar method for matrix eigenvalue problems! -- Implementation of Gauss elimination in Burnside's method -- Modular arithmetic -- Matrix eigenvalue problem in Dixon's method -- Degenerate eigenvalues -- Exercises -- Appendix 2 -- Dixon's method -- Modular characters -- Computing multiplicities -- Irreducible characters -- Computation project -- 6 Group action and symmetry projection operators -- 6.1 Group action -- 6.2 Symmetry projection operators -- 6.2.1 Construction of the symmetry transfer operators -- Construction of the operator… -- 6.2.2 The Wigner projection operator -- Hermiticity and idempotency: the eigenvalue problem -- Program for generating projection operators for molecular vibrations -- 6.2.3 The Irrep projection operator -- 6.3 The regular projection matrices: the simple characteristic -- Exercises -- 7 Construction of the irreducible representations -- 7.1 Eigenvectors of the regular Rep -- 7.1.1 Computer generation of eigenvectors of the regular Rep -- 7.2 The symmetry structure of the regular Rep eigenvectors -- 7.3 Symmetry projection on regular Rep eigenvectors -- 7.4 Computer construction of Irreps with… -- (i) Normalized symmetry-projected basis vector -- (ii) Construction of remaining Irrep basis vectors by application of other group elements -- (iii) Generate the Irrep using (13) -- 7.5 Summary of the method -- Exercise -- 8 Product groups and product representations.
8.1 Introduction -- 8.2 Subgroups and cosets -- Coset representatives -- 8.2.1 Conjugate subgroups -- Conjugacy classes of subgroups -- 8.2.2 Self-conjugate (invariant or normal) subgroups and theirquotient groups -- Groups, supergroups, and normalizers -- 8.3 Direct outer-product groups -- 8.3.1 Representations of direct outer-product groups: Kronecker-product representations -- 8.4 Semidirect product groups -- 8.5 Direct inner-product groups and their representations -- 8.6 Product representations and the Clebsch--Gordan series -- 8.6.1 Reduction of Kronecker products: the Clebsch-Gordan series -- 8.6.2 Symmetrizing Kronecker products of the same Irrep -- 8.6.3 Symmetrized pth power of an Irrep and Molien functions2 -- The Molien and generalized Molien functions -- 8.6.4 Reduction of product basis sets: Clebsch-Gordan or Wigner coeficients -- Simply reducible groups -- 8.7 Computer codes -- 8.8 Summary -- Exercises -- 9 Induced representations -- 9.1 Introduction -- 9.2 Subduced Reps and compatibility relations -- 9.3 Induction of group Reps from the Irreps of its subgroups -- 9.3.1 Inducing group Reps from Irreps of subgroups -- 9.3.2 The ground Rep -- 9.3.3 Inducing Reps of C3v from Irreps of… -- 9.4 Irreps induced from invariant subgroups -- 9.4.1 Conjugate Irreps of normal subgroups -- Equivalent and inequivalent conjugate Irreps -- 9.4.2 Group action on Irreps of normal subgroups -- Some properties of orbits and little-groups -- 9.4.3 Establishing the road map to induction of Irreps -- Conditions of irreducibility of an induced Rep… -- Condition of irreducibility for… -- Relations between Irreps of and… -- Induction of Irreps of G from allowable Irreps of the little-group… -- 9.4.4 Irrep induction procedures based on the method of little-groups -- 9.5 Examples of Irrep induction using the method of little-groups.
9.5.1 Example 1: The induced Irrep for C3v -- Discussion of Table 9.8 -- Inducing the Irreps of C3v -- 9.5.2 Example 2: induced Irreps for C4v -- Appendix Frobenius reciprocity theorem and other useful theorems -- Exercises -- 10 Crystallographic symmetry and space-groups -- 10.1 Euclidean space -- 10.1.1 Rotations and angular momentum -- Rotations in three-dimensional Euclidean space -- 10.1.2 The Euclidean group in n-dimensional space: e(n) -- 10.2 Crystallography -- 10.3 The perfect crystal -- 10.3.1 The translation group -- 10.3.2 The Holohedry group and classification of Bravais lattices -- The geometric holohedry -- 10.3.3 Lattice metric, arithmetic holohedries, and Bravais classes -- Centering and the standard (conventional) lattice -- 10.3.4 Lattice systems and Bravais classes in two and three dimensions -- 10.3.5 Unit, primitive, and Wigner--Seitz cells -- 10.3.6 The crystal -- Geometric and arithmetic crystal classes -- 10.4 Space-group operations: the Seitz operators -- Matrix form of the Seitz operators -- 10.4.1 Important properties of the Seitz operator -- 10.5 Symmorphic and nonsymmorphic space-groups -- 10.5.1 Symmorphic space-groups -- Construction of symmorphic space-groups and their notations -- 10.5.2 Nonsymmorphic space-groups -- Screw axes and glide planes -- Nonsymmorphic space-group labeling -- 10.5.3 Point-group of the crystal revisited -- 10.5.4 Classification of space-groups -- Classification of space-group types: a.ne transformations -- Arithmetic, Bravais, and geometric classes -- 10.5.5 Computer generation of space-group matrices -- 10.5.6 Subgroups and supergroups of space-groups -- Generation of k-equal space-subgroups -- The conjugation relation -- 10.6 Site-symmetries and the Wyckoff notation -- 10.6.1 Space-group action and crystallographic orbits -- Some properties of orbits.
10.6.2 Site-symmetry subgroups: stabilizers -- 10.6.3 Wyckoff positions and the Wyckoff notation -- A program for determining Wycko. positions of a given crystal -- 10.6.4 Wyckoff sets: Euclidean and affine normalizers -- The affine normalizer NA(S) -- 10.6.5 Examples of two- and three-dimensional crystals -- Two-dimensional nonsymmorphic crystals -- Three-dimensional nonsymmorphic crystals -- 10.7 Fourier space crystallography -- 10.7.1 Reciprocal space, reciprocal lattice, and diffraction patterns -- 10.7.2 Action of space-group operators in… -- 10.7.3 Equivalent space-groups, gauge transformations -- Gauge transformations and equivalent space-groups -- 10.7.4 Extinctions in Fourier space -- Exercises -- 11 Space-groups: Irreps -- 11.1 Irreps of the translation group -- 11.1.1 Brillouin zones and the reciprocal lattice -- Test for wavevectors in the first Brillouin zone -- 11.1.2 Symmetry projection operators of T and Bloch functions -- 11.1.3 Point-groups and conjugate Irreps of the translation group -- 11.1.4 Orbits and little-groups -- 11.1.5 Rectangular Brillouin zone -- Decomposition of the space-group -- 11.2 Induction of Irreps of space-groups -- 11.2.1 The method of the little-group of the first kind: projective Irreps and multiplier factor systems -- 11.2.2 Examples of symmorphic space-groups -- The two-dimensional symmorphic space-group p4mm -- A two-dimensional crystal with a symmorphic space-group p4 -- 11.2.3 Program for constructing subgroups of the wavevectors -- 11.2.4 Nonsymmorphic space-groups: Herring's method of kernel and quotient subgroups -- Herring's little-group and its Irreps -- The construction of allowable Irreps -- 11.2.5 Examples of nonsymmorphic space-groups -- The two-dimensional space-group p2mg -- Irreps of the 2D space-group p4gm -- Exercises -- 12 Time-reversal symmetry: color groups and Onsager relations.
12.1 Introduction.
Summary: Graduate textbook applying group theoretical techniques to solving symmetry related problems.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF00022232
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP00022232
Ebrary Ebrary Sudan Available
Ebrary Ebrary Tunisia Available
Total holds: 0

Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Symmetry and physics -- 1.1 Introduction -- 1.2 Hamiltonians, eigenfunctions, and eigenvalues -- 1.2.1 Examples of symmetry and conservation laws -- Translation and conservation of linear momentum -- Inversion and parity conservation -- 1.3 Symmetry operators and operator algebra -- 1.3.1 Configuration-space operators -- 1.3.2 Function-space operations -- 1.3.3 Operator algebra -- 1.4 Point-symmetry operations -- 1.5 Applications to quantum mechanics -- Exercises -- 2 Symmetry and group theory -- 2.1 Groups and their realizations -- 2.2 The symmetric group -- 2.2.1 The permutation group -- 2.3 Computational aspects -- 2.3.1 Generation of the Cayley (multiplication) table -- Rank, basis and presentation of a group -- 2.3.2 Computer generation of group elements -- 2.4 Classes -- Geometric interpretation -- 2.4.1 Computer generation of classes and class arrays -- 2.4.2 Class multiplication -- Class rearrangement theorem -- A conjugation operation simply rearranges the list of distinct elements of a class. -- 2.4.3 Computer generation of class multiplication matrices -- 2.5 Homomorphism, isomorphism, and automorphism -- 2.6 Direct- or outer-product groups -- Exercises -- 3 Group representations: concepts -- 3.1 Representations and realizations -- 3.1.1 Transformation of coordinates -- 3.1.2 Transformation of functions -- 3.2 Generation of representations on a set of basis functions -- Exercises -- 4 Group representations: formalism and methodology -- 4.1 Matrix representations -- 4.1.1 Diagonal matrix representatives -- 4.1.2 Reducible representations -- 4.1.3 The regular representation -- 4.1.4 The great orthogonality theorem -- 4.2 Character of a matrix representation -- 4.2.1 Character orthogonality relations -- 4.2.2 Character decomposition.

4.2.3 Class matrices and Dirac characters -- 4.3 Burnside's method -- Exercises -- Computational projects -- 5 Dixon's method for computing group characters -- 5.1 The eigenvalue equation modulo p -- 5.2 Dixon's method for irreducible characters -- 5.2.1 Integer polynomials modulo p -- 5.2.2 Multiplicities and the character -- 5.3 Computer codes for Dixon's method -- Appendix 1 Finding eigenvalues and eigenvectors -- The Gauss elimination method: a peculiar method for matrix eigenvalue problems! -- Implementation of Gauss elimination in Burnside's method -- Modular arithmetic -- Matrix eigenvalue problem in Dixon's method -- Degenerate eigenvalues -- Exercises -- Appendix 2 -- Dixon's method -- Modular characters -- Computing multiplicities -- Irreducible characters -- Computation project -- 6 Group action and symmetry projection operators -- 6.1 Group action -- 6.2 Symmetry projection operators -- 6.2.1 Construction of the symmetry transfer operators -- Construction of the operator… -- 6.2.2 The Wigner projection operator -- Hermiticity and idempotency: the eigenvalue problem -- Program for generating projection operators for molecular vibrations -- 6.2.3 The Irrep projection operator -- 6.3 The regular projection matrices: the simple characteristic -- Exercises -- 7 Construction of the irreducible representations -- 7.1 Eigenvectors of the regular Rep -- 7.1.1 Computer generation of eigenvectors of the regular Rep -- 7.2 The symmetry structure of the regular Rep eigenvectors -- 7.3 Symmetry projection on regular Rep eigenvectors -- 7.4 Computer construction of Irreps with… -- (i) Normalized symmetry-projected basis vector -- (ii) Construction of remaining Irrep basis vectors by application of other group elements -- (iii) Generate the Irrep using (13) -- 7.5 Summary of the method -- Exercise -- 8 Product groups and product representations.

8.1 Introduction -- 8.2 Subgroups and cosets -- Coset representatives -- 8.2.1 Conjugate subgroups -- Conjugacy classes of subgroups -- 8.2.2 Self-conjugate (invariant or normal) subgroups and theirquotient groups -- Groups, supergroups, and normalizers -- 8.3 Direct outer-product groups -- 8.3.1 Representations of direct outer-product groups: Kronecker-product representations -- 8.4 Semidirect product groups -- 8.5 Direct inner-product groups and their representations -- 8.6 Product representations and the Clebsch--Gordan series -- 8.6.1 Reduction of Kronecker products: the Clebsch-Gordan series -- 8.6.2 Symmetrizing Kronecker products of the same Irrep -- 8.6.3 Symmetrized pth power of an Irrep and Molien functions2 -- The Molien and generalized Molien functions -- 8.6.4 Reduction of product basis sets: Clebsch-Gordan or Wigner coeficients -- Simply reducible groups -- 8.7 Computer codes -- 8.8 Summary -- Exercises -- 9 Induced representations -- 9.1 Introduction -- 9.2 Subduced Reps and compatibility relations -- 9.3 Induction of group Reps from the Irreps of its subgroups -- 9.3.1 Inducing group Reps from Irreps of subgroups -- 9.3.2 The ground Rep -- 9.3.3 Inducing Reps of C3v from Irreps of… -- 9.4 Irreps induced from invariant subgroups -- 9.4.1 Conjugate Irreps of normal subgroups -- Equivalent and inequivalent conjugate Irreps -- 9.4.2 Group action on Irreps of normal subgroups -- Some properties of orbits and little-groups -- 9.4.3 Establishing the road map to induction of Irreps -- Conditions of irreducibility of an induced Rep… -- Condition of irreducibility for… -- Relations between Irreps of and… -- Induction of Irreps of G from allowable Irreps of the little-group… -- 9.4.4 Irrep induction procedures based on the method of little-groups -- 9.5 Examples of Irrep induction using the method of little-groups.

9.5.1 Example 1: The induced Irrep for C3v -- Discussion of Table 9.8 -- Inducing the Irreps of C3v -- 9.5.2 Example 2: induced Irreps for C4v -- Appendix Frobenius reciprocity theorem and other useful theorems -- Exercises -- 10 Crystallographic symmetry and space-groups -- 10.1 Euclidean space -- 10.1.1 Rotations and angular momentum -- Rotations in three-dimensional Euclidean space -- 10.1.2 The Euclidean group in n-dimensional space: e(n) -- 10.2 Crystallography -- 10.3 The perfect crystal -- 10.3.1 The translation group -- 10.3.2 The Holohedry group and classification of Bravais lattices -- The geometric holohedry -- 10.3.3 Lattice metric, arithmetic holohedries, and Bravais classes -- Centering and the standard (conventional) lattice -- 10.3.4 Lattice systems and Bravais classes in two and three dimensions -- 10.3.5 Unit, primitive, and Wigner--Seitz cells -- 10.3.6 The crystal -- Geometric and arithmetic crystal classes -- 10.4 Space-group operations: the Seitz operators -- Matrix form of the Seitz operators -- 10.4.1 Important properties of the Seitz operator -- 10.5 Symmorphic and nonsymmorphic space-groups -- 10.5.1 Symmorphic space-groups -- Construction of symmorphic space-groups and their notations -- 10.5.2 Nonsymmorphic space-groups -- Screw axes and glide planes -- Nonsymmorphic space-group labeling -- 10.5.3 Point-group of the crystal revisited -- 10.5.4 Classification of space-groups -- Classification of space-group types: a.ne transformations -- Arithmetic, Bravais, and geometric classes -- 10.5.5 Computer generation of space-group matrices -- 10.5.6 Subgroups and supergroups of space-groups -- Generation of k-equal space-subgroups -- The conjugation relation -- 10.6 Site-symmetries and the Wyckoff notation -- 10.6.1 Space-group action and crystallographic orbits -- Some properties of orbits.

10.6.2 Site-symmetry subgroups: stabilizers -- 10.6.3 Wyckoff positions and the Wyckoff notation -- A program for determining Wycko. positions of a given crystal -- 10.6.4 Wyckoff sets: Euclidean and affine normalizers -- The affine normalizer NA(S) -- 10.6.5 Examples of two- and three-dimensional crystals -- Two-dimensional nonsymmorphic crystals -- Three-dimensional nonsymmorphic crystals -- 10.7 Fourier space crystallography -- 10.7.1 Reciprocal space, reciprocal lattice, and diffraction patterns -- 10.7.2 Action of space-group operators in… -- 10.7.3 Equivalent space-groups, gauge transformations -- Gauge transformations and equivalent space-groups -- 10.7.4 Extinctions in Fourier space -- Exercises -- 11 Space-groups: Irreps -- 11.1 Irreps of the translation group -- 11.1.1 Brillouin zones and the reciprocal lattice -- Test for wavevectors in the first Brillouin zone -- 11.1.2 Symmetry projection operators of T and Bloch functions -- 11.1.3 Point-groups and conjugate Irreps of the translation group -- 11.1.4 Orbits and little-groups -- 11.1.5 Rectangular Brillouin zone -- Decomposition of the space-group -- 11.2 Induction of Irreps of space-groups -- 11.2.1 The method of the little-group of the first kind: projective Irreps and multiplier factor systems -- 11.2.2 Examples of symmorphic space-groups -- The two-dimensional symmorphic space-group p4mm -- A two-dimensional crystal with a symmorphic space-group p4 -- 11.2.3 Program for constructing subgroups of the wavevectors -- 11.2.4 Nonsymmorphic space-groups: Herring's method of kernel and quotient subgroups -- Herring's little-group and its Irreps -- The construction of allowable Irreps -- 11.2.5 Examples of nonsymmorphic space-groups -- The two-dimensional space-group p2mg -- Irreps of the 2D space-group p4gm -- Exercises -- 12 Time-reversal symmetry: color groups and Onsager relations.

12.1 Introduction.

Graduate textbook applying group theoretical techniques to solving symmetry related problems.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.