The Construction of Spin Eigenfunctions

1. Front Matter

   Pages i-xi

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2. The Spin Operator and Spin Functions

   • Ruben Pauncz

   Pages 1-13

3. Genealogical Construction of Spin Eigenfunctions

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   Pages 15-30

4. Serber Spin Functions

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   Pages 31-43

5. Projected Spin Eigen Functions

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   Pages 45-54

6. Spin-Paired Spin Eigenfunctions

   • Ruben Pauncz

   Pages 55-63

7. The Symmetric Group

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   Pages 65-81

8. Representations of S _N Generated by Spin Eigen Functions

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   Pages 83-101

9. Combination of Spatial and Spin Functions

   • Ruben Pauncz

   Pages 103-107

10. Calculation of the Hamiltonian Matrix

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    Pages 109-137

11. Spin-Coupled Functions

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    Pages 139-152

12. Solutions to the Exercises

    • Ruben Pauncz

    Pages 153-185

13. Back Matter

    Pages 187-192

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The author wrote a monograph 20 years ago on the construction of spin eigen­ functions; the monograph was published by Plenum. The aim of that mono­ graph was to present all aspects connected with the construction of spin eigen­ functions and its relation to the use of many-electron antisymmetric wavefunc­ tions. The present book is an introduction to these subjects, with an emphasis on the practical side. After the theoretical treatment, there will be many exam­ ples and exercises which will illustrate the different methods. The theory of the symmetric group and its representations generated by the different spin eigen­ functions is an other subject, this is closely related to the quantum chemical applications. Finally we will survey the calculation of the matrix elements of the Hamiltonian, using the different constructions of the spin functions. The closing chapter will deal with a new method that gained much importance recently; the spin-coupled valence bond method. Since the publication of Spin Eigenfunctions, nearly 20 years ago there have been many interesting developments in the subject; there are quite a few new algorithms for the construction of spin eigenfunctions. Moreover the use of the spin-coupled valence bond method showed the importance of using different constructions for the spin functions. The subject matter of this book has been presented in a graduate course in the Technion. The author is obliged to the graduate students Averbukh Vitali, Gokhberg Kirill, and Narevicius Edvardas for many helpful comments.

• algorithms
• chemistry
• computer
• mechanics
• physics
• quantum chemistry
• quantum mechanics
• spin
• wave

• Technion—Israel Institute of Technology, Haifa, Israel

  Ruben Pauncz

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