| Description |
xv, 415 pages : illustrations ; 24 cm |
| Series |
Springer series in solid-state sciences ; 78 |
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Springer series in solid-state sciences ; 78
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| Contents |
Contents note continued: *14.3.1.Lifshitz's Derivation of the Lifshitz Criterion -- 15.The Symmetric Group -- 15.1.The Symmetric Group (Permutation Group) -- 15.2.Irreducible Characters -- 15.3.Construction of Irreducible Representation Matrices -- 15.4.The Basis for Irreducible Representations -- 15.5.The Unitary Group and the Symmetric Group -- 15.6.The Branching Rule -- 15.7.Wavefunctions for the Configuration (nl)x -- *15.8.D(J) as Irreducible Representations of SU(2) -- *15.9.Irreducible Representations of U(m) -- Appendices -- A.The Thirty-Two Crystallographic Point Groups -- B.Character Tables for Point Groups |
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Contents note continued: 10.Molecular Vibrations -- 10.1.Normal Modes and Normal Coordinates -- 10.2.Group Theory and Normal Modes -- 10.3.Selection Rules for Infrared Absorption and Raman Scattering -- 10.4.Interaction of Electrons with Atomic Displacements -- *10.4.1.Kramers Degeneracy -- 11.Space Groups -- 11.1.Translational Symmetry of Crystals -- 11.2.Symmetry Operations in Space Groups -- 11.3.Structure of Space Groups -- 11.4.Bravais Lattices -- 11.5.Nomenclature of Space Groups -- 11.6.The Reciprocal Lattice and the Brillouin Zone -- 11.7.Irreducible Representations of the Translation Group -- 11.8.The Group of the Wavevector k and Its Irreducible Representations -- 11.9.Irreducible Representations of a Space Group -- 11.10.Double Space Groups -- 12.Electronic States in Crystals -- 12.1.Bloch Functions and E(k) Spectra -- 12.2.Examples of Energy Bands: Ge and TlBr -- 12.3.Compatibility or Connectivity Relations -- 12.4.Bloch Functions Expressed in Terms of Plane Waves -- |
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Contents note continued: 12.5.Choice of the Origin -- 12.5.1.Effect of the Choice on Bloch Wavefunctions -- 12.6.Bloch Functions Expressed in Terms of Atomic Orbitals -- 12.7.Lattice Vibrations -- 12.8.The Spin-Orbit Interaction and Double Space Groups -- 12.9.Scattering of an Electron by Lattice Vibrations -- 12.10.Interband Optical Transitions -- 12.11.Frenkel Excitons in Molecular Crystals -- *12.12.Selection Rules in Space Groups -- 12.12.1.Symmetric and Antisymmetric Product Representations -- 13.Time Reversal and Nonunitary Groups -- 13.1.Time Reversal -- 13.2.Nonunitary Groups and Corepresentations -- 13.3.Criteria for Space Groups and Examples -- 13.4.Magnetic Space Groups -- 13.5.Excitons in Magnetic Compounds; Spin Waves -- *13.5.1.Symmetry of the Hamiltonian -- 14.Landau's Theory of Phase Transitions -- 14.1.Landau's Theory of Second-Order Phase transitions -- 14.2.Crystal Structures and Spin Alignments -- *14.3.Derivation of the Lifshitz Criterion -- |
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Contents note continued: 3.4.1.Inner Product of Vectors -- 3.4.2.Orthonormal Basis -- 3.4.3.Unitary Operators and Unitary Matrices -- 3.4.4.Hermitian Operators and Hermitian Matrices -- 3.5.Eigenvalue Problems of Hermitian and Unitary Operators -- *3.6.Linear Transformation Groups -- 4.Representations of a Group I -- 4.1.Representations -- 4.1.1.Basis for a Representation -- 4.1.2.Equivalence of Representations -- 4.1.3.Reducible and Irreducible Representations -- 4.2.Irreducible Representations of the Group C[∞]v -- 4.3.Effect of Symmetry Transformation Operators on Functions -- 4.4.Representations of the Group C3v Based on Homogeneous Polynomials -- 4.5.General Representation Theory -- 4.5.1.Unitarization of a Representation -- 4.5.2.Schur's First Lemma -- 4.5.3.Schur's Second Lemma -- 4.5.4.The Great Orthogonality Theorem -- 4.6.Characters -- 4.6.1.First and Second Orthogonalities of Characters -- 4.7.Reduction of Reducible Representations -- |
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Contents note continued: 4.7.1.Restriction to a Subgroup -- 4.8.Product Representations -- 4.8.1.Symmetric and Antisymmetric Product Representations -- 4.9.Representations of a Direct-Product Group -- *4.10.The Regular Representation -- *4.11.Construction of Character Tables -- *4.12.Adjoint Representations -- *4.13.Proofs of the Theorems on Group Representations -- *4.13.1.Unitarization of a Representation -- *4.13.2.Schur's First Lemma -- *4.13.3.Schur's Second Lemma -- *4.13.4.Second Orthogonality of Characters -- 5.Representations of a Group II -- *5.1.Induced Representations -- *5.2.Irreducible Representations of a Group with an Invariant Subgroup -- *5.3.Irreducible Representations of Little Groups or Small Representations -- *5.4.Ray Representations -- *5.5.Construction of Matrices of Irreducible Ray Representations -- 6.Group Representations in Quantum Mechanics -- 6.1.Symmetry Transformations of Wavefunctions and Quantum-Mechanical Operators -- |
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Contents note continued: 6.2.Eigenstates of the Hamiltonian and Irreducibility -- 6.3.Splitting of Energy Levels by a Perturbation -- 6.4.Orthogonality of Basis Functions -- 6.5.Selection Rules -- *6.5.1.Derivation of the Selection Rule for Diagonal Matrix Elements -- 6.6.Projection Operators -- 7.The Rotation Group -- 7.1.Rotations -- 7.2.Rotation and Euler Angles -- 7.3.Rotations as Operators; Infinitesimal Rotations -- 7.4.Representation of Infinitesimal Rotations -- 7.4.1.Rotation of. Spin Functions -- 7.5.Representations of the Rotation Group -- 7.6.SU(2), SO(3) and O(3) -- 7.7.Basis of Representations -- 7.8.Spherical Harmonics -- 7.9.Orthogonality of Representation Matrices and Characters -- 7.9.1.Completeness Relation for χxJ(ω) -- 7.10.Wigner Coefficients -- 7.11.Tensor Operators -- 7.12.Operator Equivalents -- 7.13.Addition of Three Angular Momenta; Racah Coefficients -- 7.14.Electronic Wavefunctions for the Configuration (nl)x -- 7.15.Electrons and Holes -- |
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Contents note continued: 7.16.Evaluation of the Matrix Elements of Operators -- 8.Point Groups -- 8.1.Symmetry Operations in Point Groups -- 8.2.Point Groups and Their Notation -- 8.3.Class Structure in Point Groups -- 8.4.Irreducible Representations of Point Groups -- 8.5.Double-Valued Representations and Double Groups -- 8.6.Transformation of Spin and Orbital Functions -- *8.7.Constructive Derivation of Point Groups Consisting of Proper Rotations -- 9.Electronic States of Molecules -- 9.1.Molecular Orbitals -- 9.2.Diatomic Molecules: LCAO Method -- 9.3.Construction of LCAO-MO: The-π-Electron Approximation for the Benzene Molecule -- *9.3.1.Further Methods for Determining the Basis Sets -- 9.4.The Benzene Molecule (Continued) -- 9.5.Hybridized Orbitals -- 9.5.1.Methane and sp3-Hybridization -- 9.6.Ligand Field Theory -- 9.7.Multiplet Terms in Molecules -- *9.8.Clebsch--Gordan Coefficients for Simply Reducible Groups and the Wigner--Eckart Theorem -- |
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Machine generated contents note: 1.Symmetry and the Role of Group Theory -- 1.1.Arrangement of the Book -- 2.Groups -- 2.1.Definition of a Group -- 2.1.1.Multiplication Tables -- 2.1.2.Generating Elements -- *2.1.3.Commutative Groups -- 2.2.Covering Operations of Regular Polygons -- 2.3.Permutations and the Symmetric Group -- 2.4.The Rearrangement Theorem -- 2.5.Isomorphism and Homomorphism -- 2.5.1.Isomorphism -- 2.5.2.Homomorphism -- 2.5.3.Note on Mapping -- 2.6.Subgroups -- *2.7.Cosets and Coset Decomposition -- 2.8.Conjugate Elements; Classes -- *2.9.Multiplication of Classes -- *2.10.Invariant Subgroups -- *2.11.The Factor Group -- *2.11.1.The Kernel -- *2.11.2.Homomorphism Theorem -- 2.12.The Direct-Product Group -- 3.Vector Spaces -- 3.1.Vectors and Vector Spaces -- *3.1.1.Mathematical Definition of a Vector Space -- 3.1.2.Basis of a Vector Space -- 3.2.Transformation of Vectors -- 3.3.Subspaces and Invariant Subspaces -- 3.4.Metric Vector Spaces -- |
| Bibliography |
Includes bibliographical references (pages [409]-410) and index |
| Subject |
Group theory.
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Mathematical physics.
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| Author |
Onodera, Y. (Yositaka)
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Tanabe, Yukito, 1927-
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| LC no. |
95042050 |
| ISBN |
3540604456 (softcover : alk. paper) |
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