Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Young operator methods for fermion systems

  • 111 Accesses

  • 1 Citations

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.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Palting P (1995) Int J Quantum Chem 54:19

  2. 2.

    Hamermesh M (1962) Group theory and its application to physical problems. Dover, New York

  3. 3.

    Matsen FA (1964) J Phys Chem 68:3282; (1966) J Phys Chem 70:1568

  4. 4.

    Matsen FA, Cantu AA, Poshusta RD (1966) J Phys Chem 70:1558

  5. 5.

    Chen JQ (1981) New approach to the permutation group representation. Sci. and Tech Press, Shanghai

  6. 6.

    Young A (1900) Proc Lond Math Soc 33:97; (1902) Proc Load Math Soc 34:361

  7. 7.

    Rutherford DE (1968) Substitutional analysis. Hafner, New York

  8. 8.

    Pauncz R (1979) Spin eigenfunctions. Plenum Press, New York

  9. 9.

    Elliott LP, Dawber PG (1979) Symmetry in physics. Oxford Univ press, New York

  10. 10.

    Ludwig W, Falter C (1988) Symmetries in physics. Springer, New York

  11. 11.

    Poshusta RD, Kinghorn DB (1992) Int J Quantum Chem 41:15

  12. 12.

    Goddard WA III (1967) Phys Rev 157:73

  13. 13.

    Salmon WI (1974) Adv Quantum Chem 8:37

  14. 14.

    Greiner W, Muller B (1989) Theoretical quantum mechanics physics (II). Springer, New York

  15. 15.

    Matsen FA (1992) Int J Quantum Chem 41:7

  16. 16.

    Klein DJ, Seitz WA (1992) Int J Quantum Chem 41:43

  17. 17.

    Eyring H, Walter J, Kimball GE (1944) Quantum chemistry. J Wiley, New York

  18. 18.

    Matsen FA, Pauncz R (1986) The unitary group in quantum chemistry. Elsevier, Amsterdam

  19. 19.

    Salmon WI (1974) Adv Quantum Chem 8:37

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yu, Y., Palting, P. & Chiu, Y. Young operator methods for fermion systems. Theoret. Chim. Acta 94, 125–141 (1996). https://doi.org/10.1007/BF00191644

Download citation

Key words

  • Young operator
  • Conjugacy
  • Wave function