# Symmetry of Many-Electron Systems

## 1st Edition

### Physical Chemistry: A Series of Monographs

**Authors:**I. G. Kaplan

**Editors:**Ernest M. Loebl

**eBook ISBN:**9781483191737

**Imprint:**Academic Press

**Published Date:**1st January 1975

**Page Count:**384

## Description

Symmetry of Many-Electron Systems discusses the group-theoretical methods applied to physical and chemical problems. Group theory allows an individual to analyze qualitatively the elements of a certain system in scope. The text evaluates the characteristics of the Schrodinger equations. It is proved that some groups of continuous transformation from the Lie groups are useful in identifying conditions and in developing wavefunctions. A section of the book is devoted to the utilization of group-theoretical methods in quantal calculations on many-electron systems. The focus is on the use of group-theoretical methods to the classification and calculation of states of molecule. A chapter of the book gives a comprehensive discussion of the fractional parentage method. This application is used in atomic and nuclear spectroscopy. The method of employing coordinate wave functions is explained. The standard Young-Yamanouchi orthogonal representation is presented completely. The book will provide useful guides for physicists, chemists, engineers, students, and researchers in the field of physics.

## Table of Contents

Translator's Note

Preface to Russian Edition

Mathematical Apparatus

Chapter I Basic Concepts and Theorems of Group Theory

Part 1. Properties of Group Operations

Part 2. Representations of Groups

Chapter II The Permutation Group

Part 1. General Considerations

Part 2. The Standard Young-Yamanouchi Orthogonal Representation

Part 3. The Nonstandard Representation

Chapter III Groups of Linear Transformations

Part 1. Continuous Groups

Part 2. The Three-Dimensional Rotation Group

Part 3. Point Groups

Chapter IV Tensor Representations and Tensor Operators

Part 1. The Interconnection between Linear Groups and Permutation Groups

Part 2. Irreducible Tensor Operators

Symmetry and Quantal Calculations

Chapter V Principles of the Application of Group Theory to Quantum Mechanics

5.1. The Symmetry of the Schrödinger Equation and the Classification of States

5.2. Conservation Laws

5.3. Perturbation Theory

5.4. The Variation Method

5.5. Selection Rules

Chapter VI Classification of States

Part 1. Electrons in a Central Field

Part 2. The Connection between Molecular Terms and Nuclear Spin

Part 3. Classification of States in Approximate Quantal

Chapter VII The Method of Coefficients of Fractional Parentage

Part 1. Equivalent Electrons

Part 2. Configurations of Several Groups of Equivalent Electrons. A State with Arbitrary Permutational Symmetry

Part 3. Non-Vector-Coupled States

Chapter VIII Calculation of Electronic States of Molecular Systems

Part 1. The Hydrogen Molecule. Configuration Interaction

Part 2. Calculation of the Energy Matrix for an Arbitrary Molecular System

Part 3. Symmetric Systems

Part 4. The Self-Consistent Field Method

Appendix 1 Character Tables for Point Groups

Appendix 2 Matrices of Orthogonal Irreducible Representations of the Point Groups

Appendix 3 Tables for the Reduction of the Representations U[λ]2j+1 to the Group R3

Appendix 4 Character Tables for the Permutation Groups π2 to π8

Appendix 5 Matrices of the Orthogonal Irreducible Representations for the Permutation Groups π3 to π6

Appendix 6 Tables of the Matrices <r'λ"|PN-1Nab|r>[λ] for Values of N from 3 to 6

Appendix 7 Tables of the Matrices <(r'1r2)λ'λ"|PN-1Nac|r1r2>[λ] for Values of N from 3 to 6

References

Author Index

Subject Index

## Details

- No. of pages:
- 384

- Language:
- English

- Copyright:
- © Academic Press 1975

- Published:
- 1st January 1975

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483191737