http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Simmetrii︠a︡ mnogoėlektronnykh sistem. English
1 online resource (xii, 370 pages) : illustrations
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.
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