Symmetry of Many-Electron Systems

Physical Chemistry: A Series of Monographs

1st Edition - January 1, 1975
Author: I. G. Kaplan
Editor: Ernest M. Loebl
Language: English
Hardback ISBN:
9 7 8 - 0 - 1 2 - 3 9 7 1 5 0 - 0
Paperback ISBN:
9 7 8 - 1 - 4 8 3 1 - 7 5 9 2 - 8
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 9 1 7 3 - 7

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… Read more

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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.

Translator's NotePreface to Russian EditionMathematical 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 OperatorsSymmetry 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 MethodAppendix 1 Character Tables for Point GroupsAppendix 2 Matrices of Orthogonal Irreducible Representations of the Point GroupsAppendix 3 Tables for the Reduction of the Representations U[λ]2j+1 to the Group R3Appendix 4 Character Tables for the Permutation Groups π2 to π8Appendix 5 Matrices of the Orthogonal Irreducible Representations for the Permutation Groups π3 to π6Appendix 6 Tables of the Matrices [λ] for Values of N from 3 to 6Appendix 7 Tables of the Matrices [λ] for Values of N from 3 to 6ReferencesAuthor IndexSubject Index