Group Theory and Quantum Mechanics.

Format:

Book

Author/Creator:

Tinkham, Michael

Series:

Dover Books on Chemistry

Language:

English

Subjects (All):

Quantum theory.

Group theory.

Physical Description:

1 online resource

1 online resource (618 p.)

Edition:

1st ed.

Place of Publication:

Mineola, New York : Dover Publications, 1992.

Summary:

This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids.The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state

Contents:

Cover; Title Page; Copyright Page; Preface; Contents; I Introduction; 1-1 The Nature of the Problem; 1-2 The Role of Symmetry; 2 Abstract Group Theory; 2-1 Definitions and Nomenclature; 2-2 Illustrative Examples; 2-3 Rearrangement Theorem; 2-4 Cyclic Groups; 2-5 Subgroups and Cosets; 2-6 Example Groups of Finite Order; 2-7 Conjugate Elements and Class Structure; 2-8 Normal Divisors and Factor Groups; 2-9 Class Multiplication; Exercises; References; 3 Theory of Group Representations; 3-1 Definitions; 3-2 Proof of the Orthogonality Theorem; 3-3 The Character of a Representation

3-4 Construction of Character Tables3-5 Decomposition of Reducible Representations; 3-6 Application of Representation Theory in Quantum Mechanics; 3-7 Illustrative Representations of Abelian Groups; 3-8 Basis Functions for Irreducible Representations; 3-9 Direct-product Groups; 3-10 Direct-product Representations within a Group; Exercises; References; 4 Physical Applications of Group Theory; 4-1 Crystal-symmetry Operators; 4-2 The Crystallographic Point Groups; 4-3 Irreducible Representations of the Point Groups; 4-4 Elementary Representations of the Three-dimensional Rotation Group

4-5 Crystal-field Splitting of Atomic Energy Levels4-6 Intermediate Crystal-field-splitting Case; 4-7 Weak-crystal-field Case and Crystal Double Groups; 4-8 Introduction of Spin Effects in the Medium-field Case; 4-9 Group-theoretical Matrix-element Theorems; 4-10 Selection Rules and Parity; 4-11 Directed Valence; 4-12 Application of Group Theory to Directed Valence; Exercises; References; 5 Full Rotation Group and Angular Momentum; 5-1 Rotational Transformation Properties and Angular Momentum; 5-2 Continuous Groups; 5-3 Representation of Rotations through Eulerian Angles

5-4 Homomorphism with the Unitary Group5-5 Representations of the Unitary Group; 5-6 Representation of the Rotation Group by Representations of the Unitary Group; 5-7 Application of the Rotation-representation Matrices; 5-8 Vector Model for Addition of Angular Momenta; 5-9 The Wigner or Clebsch-Gordan Coefficients; 5-10 Notation, Tabulations, and Symmetry Properties of the Wigner Coefficients; 5-11 Tensor Operators; 5-12 The Wigner-Eckart Theorem; 5-13 The Racah Coefficients; 5-14 Application of Racah Coefficients; 5-15 The Rotation-Inversion Group; 5-16 Time-reversal Symmetry

5-17 More General InvariancesExercises; References; 6 Quantum Mechanics of Atoms; 6-1 Review of Elementary Atomic Structure and Nomenclature; 6-2 The Hamiltonian; 6-3 Approximate Eigenfunctions; 6-4 Calculation of Matrix Elements between Determinantal Wavefunctions; 6-5 Hartree-Fock Method; 6-6 Calculation of L-S-term Energies; 6-7 Evaluation of Matrix Elements of the Energy; 6-8 Eigenfunctions and Angular-momentum Operations; 6-9 Calculation of Fine Structure; 6-10 Zeeman Effect; 6-11 Magnetic Hyperfine Structure; 6-12 Electric Hyperfine Structure; Exercises; References

7 Molecular Quantum Mechanics

Notes:

Description based upon print version of record

Description based on publisher supplied metadata and other sources.

ISBN:

9780486131665

0486131661

9781621985938

1621985938

OCLC:

868270192