Symmetry of Many-Electron Systems
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Symmetry of Many-Electron Systems

Physical Chemistry: A Series of Monographs

1st Edition - January 1, 1975

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  • Author: I. G. Kaplan
  • eBook ISBN: 9781483191737

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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 [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


Product details

  • No. of pages: 384
  • Language: English
  • Copyright: © Academic Press 1975
  • Published: January 1, 1975
  • Imprint: Academic Press
  • eBook ISBN: 9781483191737

About the Author

I. G. Kaplan

About the Editor

Ernest M. Loebl

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