Symmetry of many-electron systems
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...
| Uniform Title: | Simmetrii{u0361}a mnogoėlektronnykh sistem. English |
|---|---|
| Main Author: | Kaplan, I. G. |
| Other Authors: | Gerratt, J.,, ScienceDirect (Online service) |
| Format: | eBook |
| Language: | English Russian |
| Published: |
New York :
Academic Press,
1975.
|
| Physical Description: |
1 online resource (xii, 370 pages) : illustrations. |
| Series: |
Physical chemistry ;
volume 34. |
| Subjects: |
Table of Contents:
- Front Cover; Symmetry of Many-Electron Systems; Copyright Page; Table of Contents; Translator's Note; Preface to Russian Edition; PART I: MATHEMATICAL APPARATUS; CHAPTER I. Basic Concepts and Theorems of Group Theory; Part 1. Properties of Group Operations; 1.1. Group Postulates; 1.2. Examples of Groups; 1.3. Isomorphism and Homomorphism; 1.4. Subgroups and Cosets; 1.5. Conjugate Elements. Classes; 1.6. Invariant Subgroups. Factor Groups; 1.7. Direct Products of Groups; 1.8. The Semidirect Product; Part 2. Representations of Groups; 1.9. Definition; 1.10. Vector Spaces.
- 1.11. Reducibility of Representations1.12. Properties of Irreducible Representations; 1.13. Characters; 1.14. The Calculation of the Characters of Irreducible Representations; 1.15. The Decomposition of a Reducible Representation; 1.16. The Direct Product of Representations; 1.17. Clebsch-Gordan Coefficients; 1.18. The Regular Representation; 1.19. The Construction of Basis Functions for Irreducible Representations; CHAPTER II. The Permutation Group; Part 1. General Considerations; 2.1. Operations with Permutations; 2.2. Classes; 2.3. Young Diagrams and Irreducible Representations.
- Part 2. The Standard Young-Yamanouchi OrthogonalRepresentation2.4. Young Tableaux; 2.5. Explicit Determination of the Matrices of the Standard Representation; 2.6. The Conjugate Representation; 2.7. The Construction of an Antisymmetric Function from the Basis Functions for Two Conjugate Representations; 2.8. Young Operators; 2.9. The Construction of Basis Functions for a StandardRepresentation from a Product of N Orthogonal Functions; Part 3. The Nonstandard Representation; 2.10. Definition; 2.11. The Transformation Matrix; 2.12. Some Generalizations.
- 2.13. Young Operators in a Nonstandard RepresentationCHAPTER III. Groups of Linear Transformations; Part 1. Continuous Groups; 3.1. Definition. Distinctive Features of Continuous Groups; 3.2. Examples of Linear Groups; 3.3. Infinitesimal Operators; Part 2. The Three-Dimensional Rotation Group; 3.4. Rotation Operators and Angular Momentum Operators; 3.5. Irreducible Representations; 3.6. Reduction of the Direct Product of Two Irreducible Representations; 3.7. Reduction of t he Direct Product of k Irreducible Representations. 3n-j Symbols; Part 3. Point Groups.