Representations of the Symmetric Group Generated by the Spin Eigenfunctions

  • Ruben Pauncz


In the previous chapter we have seen that the different irreducible representations of the symmetric group can be characterized by the different Young shapes. The notion of the Young tableau was helpful for the construction of the orthogonal and natural representation. In this chapter we shall consider the behavior of the spin eigenfunctions under the operations of the permutations of the electronic coordinates, and we shall show that they generate irreducible representations of the symmetric group; the latter can be characterized by Young shapes having not more than two rows. We shall also establish a one-to-one correspondence between the Young tableaux and the functions generated in the different methods. The representation matrices will play an important role in the calculation of the matrix elements of the Hamiltonian; the one-to-one correspondence gives us new and effective methods for the construction of spin eigenfunctions.


Representation Matrix Transformation Matrix Symmetric Group Representation Matrice Young Tableau 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T. Yamanouchi, Proc. Phys. Math. Soc. Jpn. 18, 623 (1936).Google Scholar
  2. 2.
    M. Kotani, A. Amemiya, E. Ishiguro, and T. Kimura, Tables of Molecular Integrals, 2nd ed., Maruzen, Tokyo (1963), Chapter 1.Google Scholar
  3. 3.
    R. Pauncz, Alternant Molecular Orbital Method, W. B. Saunders, Philadelphia (1967), Appendix 2, p. 216.Google Scholar
  4. 4.
    S. Rettrup, Chem. Phys. Lett. 47, 59 (1977).CrossRefGoogle Scholar
  5. 5.
    R. Pauncz, Chem. Phys. Lett. 31, 443 (1975).CrossRefGoogle Scholar
  6. 6. (a).
    T. Yamanouchi, Proc. Phys. Math. Soc. Jpn. 19, 436 (1937)Google Scholar
  7. 6. (b).
    F. Hund, as quoted by E. Wigner, Phys. Rev. 51, 947 (1937).CrossRefGoogle Scholar
  8. 7.
    F. E. Harris, Adv. Quantum Chem. 3 61 (1967).CrossRefGoogle Scholar
  9. 8.
    W. I. Salmon, Adv. Quantum Chem. 8 37 (1974).CrossRefGoogle Scholar
  10. 9.
    W. I. Salmon, K. Ruedenberg, and L. M. Cheung, J. Chem. Phys. 57 2787 (1972).CrossRefGoogle Scholar
  11. 10.
    E. M. Corson, Perturbation Methods in the Quantum Mechanics of n-Electron Systems, Blackie and Son, London (1951), p. 217.Google Scholar
  12. 11.
    L. F. Mattheiss, Quart. Progr. Rep., Solid State Molecular Theory Group MIT 34 58, (1959).Google Scholar
  13. 12. (a).
    S. Wilson, Chem. Phys. Lett. 49 168 (1977)CrossRefGoogle Scholar
  14. 12. (b).
    S. Wilson, J. Chem. Phys. 67, 5088 (1977).CrossRefGoogle Scholar
  15. 13.
    J. P. Elliott, J. Hope, and H. A. Jahn, Philos. Trans. R. Soc. London Ser. A 246, 241 (1953).CrossRefGoogle Scholar
  16. 14.
    J. Gerratt, Adv. At. Mol. Phys. 7, 141 (1971).CrossRefGoogle Scholar
  17. 15.
    D. E. Littlewood, The Theory of Group Characters, Clarendon Press, Oxford (1950), p. 94.Google Scholar
  18. 16.
    I. G. Kaplan, Sov. Phys.-JETP 14, 401 (1962).Google Scholar
  19. 17.
    H. Horie, J. Phys. Soc. Jpn. 19, 1783 (1964).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • Ruben Pauncz
    • 1
  1. 1.Technion-Israel Institute of TechnologyHaifaIsrael

Personalised recommendations