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Theoretica chimica acta

, Volume 94, Issue 3, pp 125–141 | Cite as

Young operator methods for fermion systems

  • Yaxiong Yu
  • Pancracio Palting
  • Ying-Nan Chiu
Article

Summary

Alternative methods to the standard Young technique for the construction of Fermion wave functions in the spin orbital formalism are presented and shown to be equivalent to the standard technique. To develop these methods: (i) the starting or primitive function is factored into spin and spatial parts, (ii) the conjugacy feature required to satisfy the antisymmetry principle is exploited, (iii) the necessary commutation relations with the Fermion antisymmetrizer are shown to hold and (iv) the one-to-one correspondence between the independent picture of the Young tableaux and the independent Slater determinants is used. This last feature has the advantage of reducing all three methods to rapid efficient graphical procedures. Each method is analyzed to consider the amount of labor involved to carry it out. Several examples of the methods are given for constructing both electronic wave functions and spin functions.

Key words

Young operator Conjugacy Wave function 

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References

  1. 1.
    Palting P (1995) Int J Quantum Chem 54:19Google Scholar
  2. 2.
    Hamermesh M (1962) Group theory and its application to physical problems. Dover, New YorkGoogle Scholar
  3. 3.
    Matsen FA (1964) J Phys Chem 68:3282; (1966) J Phys Chem 70:1568Google Scholar
  4. 4.
    Matsen FA, Cantu AA, Poshusta RD (1966) J Phys Chem 70:1558Google Scholar
  5. 5.
    Chen JQ (1981) New approach to the permutation group representation. Sci. and Tech Press, ShanghaiGoogle Scholar
  6. 6.
    Young A (1900) Proc Lond Math Soc 33:97; (1902) Proc Load Math Soc 34:361Google Scholar
  7. 7.
    Rutherford DE (1968) Substitutional analysis. Hafner, New YorkGoogle Scholar
  8. 8.
    Pauncz R (1979) Spin eigenfunctions. Plenum Press, New YorkGoogle Scholar
  9. 9.
    Elliott LP, Dawber PG (1979) Symmetry in physics. Oxford Univ press, New YorkGoogle Scholar
  10. 10.
    Ludwig W, Falter C (1988) Symmetries in physics. Springer, New YorkGoogle Scholar
  11. 11.
    Poshusta RD, Kinghorn DB (1992) Int J Quantum Chem 41:15Google Scholar
  12. 12.
    Goddard WA III (1967) Phys Rev 157:73Google Scholar
  13. 13.
    Salmon WI (1974) Adv Quantum Chem 8:37Google Scholar
  14. 14.
    Greiner W, Muller B (1989) Theoretical quantum mechanics physics (II). Springer, New YorkGoogle Scholar
  15. 15.
    Matsen FA (1992) Int J Quantum Chem 41:7Google Scholar
  16. 16.
    Klein DJ, Seitz WA (1992) Int J Quantum Chem 41:43Google Scholar
  17. 17.
    Eyring H, Walter J, Kimball GE (1944) Quantum chemistry. J Wiley, New YorkGoogle Scholar
  18. 18.
    Matsen FA, Pauncz R (1986) The unitary group in quantum chemistry. Elsevier, AmsterdamGoogle Scholar
  19. 19.
    Salmon WI (1974) Adv Quantum Chem 8:37Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Yaxiong Yu
    • 1
  • Pancracio Palting
    • 1
  • Ying-Nan Chiu
    • 1
  1. 1.Department of ChemistryThe Catholic University of AmericaWashingtonUSA

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