Spin Eigenfunctions - Pauncz, Ruben

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Sommaire:
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. Constructionof 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.