Spin Eigenfunctions : Construction and Use / by Ruben Pauncz.
1. Introduction.- 1.1. Electronic States with Definite Multiplicities.- 1.2. Basic Facts with Respect to the Spin.- 1.3. Spin Operators and Functions for One Electron.- 1.4. Addition Theorem of Angular Momenta.- References.- 2. Construction of Spin Eigenfunctions from the Products of One-Electron Sp...
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Boston, MA :
Springer US,
1979.
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Table of Contents:
- 1. Introduction
- 2. Construction of Spin Eigenfunctions from the Products of One-Electron Spin Functions
- 3. Construction of Spin Eigenfunctions from the Products of Two-Electron Spin Eigenfunctions
- 4. Construction of Spin Eigenfunctions by the Projection Operator Method
- 5. Spin-Paired Spin Eigenfunctions
- 6. Basic Notions of the Theory of the Symmetric Group
- 7. Representations of the Symmetric Group Generated by the Spin Eigenfunctions
- 8. Representations of the Symmetric Group Generated by the Projected Spin Functions and Valence Bond Functions
- 9. Combination of Spatial and Spin Functions; Calculation of the Matrix Elements of Operators
- 10. Calculation of the Matrix Elements of the Hamiltonian; Orthogonal Spin Functions
- 11. Calculation of the Matrix Elements of the Hamiltonian; Nonorthogonal Spin Functions
- 12. Spin-Free Quantum Chemistry
- 13. Matrix Elements of the Hamiltonian and the Representation of the Unitary Group
- Appendix 1. Some Basic Algebraic Notions
- A.1.1. Introduction
- A.1.2. Frobenius or Group Algebra; Convolution Algebra
- A.1.2.1. Invariant Mean
- A.1.2.2. Frobenius or Group Algebra
- A.1.2.3. Convolution Algebra
- A.1.3. Some Algebraic Notions
- A.1.4. The Centrum of the Algebra
- A.1.5. Irreducible Representations; Schur's Lemma
- A.1.6. The Matric Basis
- A.1.7. Symmetry Adaptation
- A.1.8. Wigner-Eckart Theorem
- References
- Appendix 2. The Coset Representation
- A.2.1. Introduction
- A.2.2. The Character of an Element g in the Coset Representation.
- Appendix 3. Double Coset
- A.3.1. The Double Coset Decomposition
- A.3.2. The Number of Elements in a Double Coset
- Appendix 4. The Method of Spinor Invariants
- A.4.1. Spinors and Their Transformation Properties
- A.4.2. The Method of Spinor Invariants
- A.4.3. Construction of the Genealogical Spin Functions by the Method of Spinor Invariants
- A.4.4. Normalization Factors
- A.4.5. Construction of the Serber Functions by the Method of Spinor Invariants
- A.4.6. Singlet Functions as Spinor Invariants
- References
- A.5.1. The Formalism of Second Quantization
- A.5.2. Representation of the Spin Operators in the Second-Quantization Formalism
- A.5.3. Review of the Papers That Use the Second-Quantization Formalism for the Construction of Spin Eigenfunctions
- A.5.3.1. Genealogical Construction
- A.5.3.2. Projection Operator Method
- A.5.3.3. Valence Bond Method
- A.5.3.4. The Occupation-Branching-Number Representation
- References
- Appendix 6. Table of Sanibel Coefficients
- Reference
- Author Index.