Group Theory and Quantum Mechanics

ISBN-10: 0486432475
ISBN-13: 9780486432472
Edition: 2003
Authors: Michael Tinkham
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Description: This graduate-level text develops aspects of group theory most relevant to physics and chemistry and illustrates their applications to quantum mechanics: abstract group theory, theory of group representations, physical applications of group theory,  More...

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Book details

List price: $24.95
Copyright year: 2003
Publisher: Dover Publications, Incorporated
Publication date: 12/17/2003
Binding: Paperback
Pages: 352
Size: 5.25" wide x 8.25" long x 0.75" tall
Weight: 0.792
Language: English

This graduate-level text develops aspects of group theory most relevant to physics and chemistry and illustrates their applications to quantum mechanics: abstract group theory, theory of group representations, physical applications of group theory, full rotation group and angular momentum, quantum mechanics of atoms, molecular quantum mechanics, and solid-state theory. 1964 edition.

Preface
Introduction
The Nature of the Problem
The Role of Symmetry
Abstract Group Theory
Definitions and Nomenclature
Illustrative Examples
Rearrangement Theorem
Cyclic Groups
Subgroups and Cosets
Example Groups of Finite Order
Conjugate Elements and Class Structure
Normal Divisors and Factor Groups
Class Multiplication
Exercises
References
Theory of Group Representations
Definitions
Proof of the Orthogonality Theorem
The Character of a Representation
Construction of Character Tables
Decomposition of Reducible Representations
Application of Representation Theory in Quantum Mechanics
Illustrative Representations of Abelian Groups
Basis Functions for Irreducible Representations
Direct-product Groups
Direct-product Representations within a Group
Exercises
References
Physical Applications of Group Theory
Crystal-symmetry Operators
The Crystallographic Point Groups
Irreducible Representations of the Point Groups
Elementary Representations of the Three-dimensional Rotation Group
Crystal-field Splitting of Atomic Energy Levels
Intermediate Crystal-field-splitting Case
Weak-crystal-field Case and Crystal Double Groups
Introduction of Spin Effects in the Medium-field Case
Group-theoretical Matrix-element Theorems
Selection Rules and Parity
Directed Valence
Application of Group Theory to Directed Valence
Exercises
References
Full Rotation Group and Angular Momentum
Rotational Transformation Properties and Angular Momentum
Continuous Groups
Representation of Rotations through Eulerian Angles
Homomorphism with the Unitary Group
Representations of the Unitary Group
Representation of the Rotation Group by Representations of the Unitary Group
Application of the Rotation-representation Matrices
Vector Model for Addition of Angular Momenta
The Wigner or Clebsch-Gordan Coefficients
Notation, Tabulations, and Symmetry Properties of the Wigner Coefficients
Tensor Operators
The Wigner-Eckart Theorem
The Racah Coefficients
Application of Racah Coefficients
The Rotation-Inversion Group
Time-reversal Symmetry
More General Invariances
Exercises
References
Quantum Mechanics of Atoms
Review of Elementary Atomic Structure and Nomenclature
The Hamiltonian
Approximate Eigenfunctions
Calculation of Matrix Elements between Determinantal Wavefunctions
Hartree-Fock Method
Calculation of L-S-term Energies
Evaluation of Matrix Elements of the Energy
Eigenfunctions and Angular-momentum Operations
Calculation of Fine Structure
Zeeman Effect
Magnetic Hyperfine Structure
Electric Hyperfine Structure
Exercises
References
Molecular Quantum Mechanics
Born-Oppenheimer Approximation
Simple Electronic Eigenfunctions
Irreducible Representations for Linear Molecules
The Hydrogen Molecule
Molecular Orbitals
Heitler-London Method
Orthogonal Atomic Orbitals
Group Theory and Molecular Orbitals
Selection Rules for Electronic Transitions
Vibration of Diatomic Molecules
Normal Modes in Polyatomic Molecules
Group Theory and Normal Modes
Selection Rules for Vibrational Transitions
Molecular Rotation
Effect of Nuclear Statistics on Molecular Rotation
Asymmetric Rotor
Vibration-Rotation Interaction
Rotation-Electronic Coupling
Exercises
References
Solid-state Theory
Symmetry Properties in Solids
The Reciprocal Lattice and Brillouin Zones
Form of Energy-band Wavefunctions
Crystal Symmetry and the Group of the k Vector
Pictorial Consideration of Eigenfunctions
Formal Consideration of Degeneracy and Compatibility
Group Theory and the Plane-wave Approximation
Connection between Tight- and Loose-binding Approximations
Spin-orbit Coupling in Band Theory
Time Reversal in Band Theory
Magnetic Crystal Groups
Symmetries of Magnetic Structures
The Landau Theory of Second-order Phase Transitions
Irreducible Representations of Magnetic Groups
Exercises
References
Appendix
Review of Vectors, Vector Spaces, and Matrices
Character Tables for Point-symmetry Groups
Tables of c[superscript k] and a[superscript k] Coefficients for s, p, and d Electrons
Index

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