Skip to main content
SpringerLink
Log in

Semi-classical limit theorems for Hartree-Fock theory

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Consider a large number of electrons with Coulomb repulsion moving under the influence of static nuclei. It is assumed the potentials due to the nuclei are Coulombic away from their centers but are smooth at the centers, so no singularities exist. The author shows that the exchange energy for the Hartree-Fock ground state of this system converges in a suitable limit to the formula obtained by Dirac for exchange energy as an integral of the one body density.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Carmona, R.: Regularity properties of Schrödinger and Dirchlet semi-groups. J. Functional Anal.33, 259–296 (1976)

    Google Scholar 

  2. Conlon, J.: A refinement of the Thomas-Fermi approximation for theN body problem. J. Math. Phys. (to appear)

  3. Cwickel, M.: Weak type estimates for singular values and the number of bound states of Schrödinger operators. Ann. Math.106, 93–100 (1977)

    Google Scholar 

  4. Dirac, P.: Note on exchange phenomena in the Thomas atom. Proc. Cambridge Philos. Soc.26, 376–385 (1930)

    Google Scholar 

  5. Dunford, N., Schwartz, J.: Linear operators, Vol. I. New York: Interscience 1963

    Google Scholar 

  6. Lieb, E.: The stability of matter. Rev. Mod. Phys.48, 553–569 (1976)

    Google Scholar 

  7. Lieb, E.: A lower bound for Coulomb energies. Phys. Lett.70A, 444–446 (1979)

    Google Scholar 

  8. Lieb, E.: Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys.53, 603–641 (1981)

    Google Scholar 

  9. Lieb, E.: AnL p bound for the Reisz and Bessel potentials of orthonormal functions. Preprint 1982

  10. Lieb, E., Oxford, S.: An improved lower bound on the indirect Coulomb energy. Int. J. Quant. Chem.19, 427–439 (1981)

    Google Scholar 

  11. Lieb, E., Simon, B.: The Hartree-Fock theory for Coulomb systems. Commun. Math. Phys.53, 185–194 (1977)

    Google Scholar 

  12. Lieb, E., Simon, B.: The Thomas-Fermi theory of atoms, molecules, and solids. Adv. Math.23, 22–116 (1977)

    Google Scholar 

  13. Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. II. New York: Academic Press 1975

    Google Scholar 

  14. Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. IV. New York: Academic Press 1978

    Google Scholar 

  15. Simon, B.: Functional integration and quantum physics. New York: Academic Press 1979

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Missouri, 65211, Columbia, MO, USA

    Joseph G. Conlon

Authors
  1. Joseph G. Conlon
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by B. Simon

Research supported by NSF Grant No. MCS8100761

Rights and permissions

Reprints and permissions

About this article

Cite this article

Conlon, J.G. Semi-classical limit theorems for Hartree-Fock theory. Commun.Math. Phys. 88, 133–150 (1983). https://doi.org/10.1007/BF01206884

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01206884

Keywords

Search

Navigation