Group theory and quantum mechanics

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Group theory and quantum mechanics / Michael Tinkham

資料種別:: 図書
出版情報:: New York : McGraw-Hill, c1964
形態:: xii, 340 p ; 24 cm
シリーズ名:: International series in pure and applied physics <BA00024035>
著者名:: Tinkham, Michael <DA00792940>
ISBN:: 9780070648951 [0070648956]
書誌ID:: BA04366132

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注記:

Includes bibliographies and index

主題:

Groups, Theory of; Quantum theory

言語:

英語

目次情報:

Preface

Introduction / 1：

The Nature of the Problem / 1-1：

The Role of Symmetry / 1-2：

Abstract Group Theory / 2：

Definitions and Nomenclature / 2-1：

Illustrative Examples / 2-2：

Rearrangement Theorem / 2-3：

Cyclic Groups / 2-4：

Subgroups and Cosets / 2-5：

Example Groups of Finite Order / 2-6：

Conjugate Elements and Class Structure / 2-7：

Normal Divisors and Factor Groups / 2-8：

Class Multiplication / 2-9：

Exercises

References

Theory of Group Representations / 3：

Definitions / 3-1：

Proof of the Orthogonality Theorem / 3-2：

The Character of a Representation / 3-3：

Construction of Character Tables / 3-4：

Decomposition of Reducible Representations / 3-5：

Application of Representation Theory in Quantum Mechanics / 3-6：

Illustrative Representations of Abelian Groups / 3-7：

Basis Functions for Irreducible Representations / 3-8：

Direct-product Groups / 3-9：

Direct-product Representations within a Group / 3-10：

Physical Applications of Group Theory / 4：

Crystal-symmetry Operators / 4-1：

The Crystallographic Point Groups / 4-2：

Irreducible Representations of the Point Groups / 4-3：

Elementary Representations of the Three-dimensional Rotation Group / 4-4：

Crystal-field Splitting of Atomic Energy Levels / 4-5：

Intermediate Crystal-field-splitting Case / 4-6：

Weak-crystal-field Case and Crystal Double Groups / 4-7：

Introduction of Spin Effects in the Medium-field Case / 4-8：

Group-theoretical Matrix-element Theorems / 4-9：

Selection Rules and Parity / 4-10：

Directed Valence / 4-11：

Application of Group Theory to Directed Valence / 4-12：

Full Rotation Group and Angular Momentum / 5：

Rotational Transformation Properties and Angular Momentum / 5-1：

Continuous Groups / 5-2：

Representation of Rotations through Eulerian Angles / 5-3：

Homomorphism with the Unitary Group / 5-4：

Representations of the Unitary Group / 5-5：

Representation of the Rotation Group by Representations of the Unitary Group / 5-6：

Application of the Rotation-representation Matrices / 5-7：

Vector Model for Addition of Angular Momenta / 5-8：

The Wigner or Clebsch-Gordan Coefficients / 5-9：

Notation, Tabulations, and Symmetry Properties of the Wigner Coefficients / 5-10：

Tensor Operators / 5-11：

The Wigner-Eckart Theorem / 5-12：

The Racah Coefficients / 5-13：

Application of Racah Coefficients / 5-14：

The Rotation-Inversion Group / 5-15：

Time-reversal Symmetry / 5-16：

More General Invariances / 5-17：

Quantum Mechanics of Atoms / 6：

Review of Elementary Atomic Structure and Nomenclature / 6-1：

The Hamiltonian / 6-2：

Approximate Eigenfunctions / 6-3：

Calculation of Matrix Elements between Determinantal Wavefunctions / 6-4：

Hartree-Fock Method / 6-5：

Calculation of L-S-term Energies / 6-6：

Evaluation of Matrix Elements of the Energy / 6-7：

Eigenfunctions and Angular-momentum Operations / 6-8：

Calculation of Fine Structure / 6-9：

Zeeman Effect / 6-10：

Magnetic Hyperfine Structure / 6-11：

Electric Hyperfine Structure / 6-12：

Molecular Quantum Mechanics / 7：

Born-Oppenheimer Approximation / 7-1：

Simple Electronic Eigenfunctions / 7-2：

Irreducible Representations for Linear Molecules / 7-3：

The Hydrogen Molecule / 7-4：

Molecular Orbitals / 7-5：

Heitler-London Method / 7-6：

Orthogonal Atomic Orbitals / 7-7：

Group Theory and Molecular Orbitals / 7-8：

Selection Rules for Electronic Transitions / 7-9：

Vibration of Diatomic Molecules / 7-10：

Normal Modes in Polyatomic Molecules / 7-11：

Group Theory and Normal Modes / 7-12：

Selection Rules for Vibrational Transitions / 7-13：

Molecular Rotation / 7-14：

Effect of Nuclear Statistics on Molecular Rotation / 7-15：

Asymmetric Rotor / 7-16：

Vibration-Rotation Interaction / 7-17：

Rotation-Electronic Coupling / 7-18：

Solid-state Theory / 8：

Symmetry Properties in Solids / 8-1：

The Reciprocal Lattice and Brillouin Zones / 8-2：

Form of Energy-band Wavefunctions / 8-3：

Crystal Symmetry and the Group of the k Vector / 8-4：

Pictorial Consideration of Eigenfunctions / 8-5：

Formal Consideration of Degeneracy and Compatibility / 8-6：

Group Theory and the Plane-wave Approximation / 8-7：

Connection between Tight- and Loose-binding Approximations / 8-8：

Spin-orbit Coupling in Band Theory / 8-9：

Time Reversal in Band Theory / 8-10：

Magnetic Crystal Groups / 8-11：

Symmetries of Magnetic Structures / 8-12：

The Landau Theory of Second-order Phase Transitions / 8-13：

Irreducible Representations of Magnetic Groups / 8-14：

Appendix

Review of Vectors, Vector Spaces, and Matrices / A：

Character Tables for Point-symmetry Groups / B：

Tables of c[superscript k] and a[superscript k] Coefficients for s, p, and d Electrons / C：

Index

Preface

Introduction / 1：

The Nature of the Problem / 1-1：

The Role of Symmetry / 1-2：

Abstract Group Theory / 2：

Definitions and Nomenclature / 2-1：

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