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[null,"1.","Record Nr.",null,"UNINA990000734400403321"]
[null,null,"Autore",null,"Magrini, Gigliola"]
[null,null,"Titolo",null,"Il giardino nel clima e nel paesaggio / Gigliola Magrini"]
[null,null,"Pubbl/distr/stampa",null,"Milano : Goerlich, 1967"]
[null,null,"Descrizione fisica",null,"140 p. : ill. ; 29 cm"]
[null,null,"Locazione",null,"FARBC"]
[null,null,"Collocazione",null,"VIL.GI C 30"]
[null,null,"Lingua di pubblicazione",null,"Italiano"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,"2.","Record Nr.",null,"UNINA9910967032403321"]
[null,null,"Autore",null,"Inui Teturo"]
[null,null,"Titolo",null,"Group Theory and Its Applications in Physics / / by Teturo Inui, Yukito Tanabe, Yositaka Onodera"]
[null,null,"Pubbl/distr/stampa",null,"Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1990"]
[null,null,"ISBN",null,"3-642-80021-1"]
[null,null,"Edizione",null,"[1st ed. 1990.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XV, 397 p.)"]
[null,null,"Collana",null,"Springer Series in Solid-State Sciences, , 2197-4179 ; ; 78"]
[null,null,"Disciplina",null,"530.1/522"]
[null,null,"Soggetti",null,"Mathematical physics"]
[{"$nulls":4},"Crystallography"]
[{"$nulls":4},"Atoms"]
[{"$nulls":4},"Molecules"]
[{"$nulls":4},"Mathematical Methods in Physics"]
[{"$nulls":4},"Theoretical, Mathematical and Computational Physics"]
[{"$nulls":4},"Crystallography and Scattering Methods"]
[{"$nulls":4},"Atomic, Molecular and Chemical Physics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"With 72 Figures.\""]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"1. Symmetry and the Role of Group Theory -- 1.1 Arrangement of the Book -- 2. Groups -- 2.1 Definition of a Group -- 2.1.1 Multiplication Tables -- 2.1.2 Generating Elements -- 2.1.3 Commutative Groups -- 2.2 Covering Operations of Regular Polygons -- 2.3 Permutations and the Symmetric Group -- 2.4 The Rearrangement Theorem -- 2.5 Isomorphism and Homomorphism -- 2.5.1 Isomorphism -- 2.5.2 Homomorphism -- 2.5.3 Note on Mapping -- 2.6 Subgroups -- 2.7 Cosets and Coset Decomposition -- 2.8 Conjugate Elements; Classes -- 2.9 Multiplication of Classes -- 2.10 Invariant Subgroups -- 2.11 The Factor Group -- 2.11.1 The Kernel -- 2.11.2 Homomorphism Theorem -- 2.12 The Direct-Product Group -- 3. Vector Spaces -- 3.1 Vectors and Vector Spaces -- 3.1.1 Mathematical Definition of a Vector Space -- 3.1.2 Basis of a Vector Space -- 3.2 Transformation of Vectors -- 3.3 Subspaces and Invariant Subspaces -- 3.4 Metric Vector Spaces -- 3.4.1 Inner Product of Vectors -- 3.4.2 Orthonormal Basis -- 3.4.3 Unitary Operators and Unitary Matrices -- 3.4.4 Hermitian Operators and Hermitian Matrices -- 3.5 Eigenvalue Problems of Hermitian and Unitary Operators -- 3.6 Linear Transformation Groups "]
[{"$nulls":4},"-- 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 T -- 4.6 Characters -- 4.6.1 First and Second Orthogonalities of Characters -- 4.7 Reduction ofReducible Representations -- 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 -- 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 XJ(?) -- 7.10 Wigner Coefficients -- 7.11 Tensor Operators -- 7.12 Operator Equivalents -- 7.13 Addition of Three Angular Momenta;Racah Coefficients -- 7.14Electronic Wavefunctions for the Configuration (nl)x -- 7.15 Electrons and Holes -- 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 ?-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 -- 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 "]
[{"$nulls":4},"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 TIBr -- 12.3 Compatibility or Connectivity Relations -- 12.4 Bloch Functions Expressed in Terms of Plane Waves -- 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 -- 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 -- Answers and Hints to the Exercises -- Motifs of the Family Crests -- References."]
[null,null,null,"Sommario/riassunto","This book has been written to introduce readers to group theory and its ap­ plications in atomic physics, molecular physics, and solid-state physics. The first Japanese edition was published in 1976. The present English edi­ tion has been translated by the authors from the revised and enlarged edition of 1980. In translation, slight modifications have been made in. Chaps. 8 and 14 to update and condense the contents, together with some minor additions and improvements throughout the volume. The authors cordially thank Professor J. L. Birman and Professor M. Car­ dona, who encouraged them to prepare the English translation. Tokyo, January 1990 T. Inui . Y. Tanabe Y. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics. Group theory is, in a nutshell, the mathematics of symmetry. It has three main areas of application in modern physics. The first originates from early studies of crystal morphology and constitutes a framework for classical crystal physics. The analysis of the symmetry of tensors representing macroscopic physical properties (such as elastic constants) belongs to this category. The sec­ ond area was enunciated by E. Wigner (1926) as a powerful means of handling quantum-mechanical problems and was first applied in this sense to the analysis of atomic spectra. Soon, H."]