Skip to main content
SpringerLink
Log in

Hartree-Fock approximation for the one-dimensional electron gas

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The Hartree-Fock calculation on the one-dimensional electron gas is done on the basis of the method analogous to that applied by Bloch and Wigner and Seitz for the three-dimensional gas. The boundary conditions of the standing wave are taken for the wave function and the bare Coulomb interaction between electrons is assumed. The parameterr s of the three-dimensional gas is replaced by the ratio between the cross-section radius and the length of the potential tube filled by the one-dimensional gas. Excepting for a special case of the excitement of an electron pair put on one electron level the excitation energies of the non-magnetic gas are found to be very much higher than these of the ferromagnetic gas. A similar relation holds between the ground state energies of the non-magnetic and magnetic gases.

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. Kuhn, H.: J. Chem. Phys.16, 840 (1948);17, 1198 (1949); Helv. Chim. Acta31, 1441 (1948);32, 2247 (1949);34, 1308 (1951)

    Google Scholar 

  2. Ham, N.S., Ruedenberg, K.: J. Chem. Phys.25, 1 (1956);25, 13 (1956)

    Google Scholar 

  3. Olszewski, S.: Acta Phys. Polon. A42, 563 (1972)

    Google Scholar 

  4. Tomonaga, S.: Prog. Theor. Phys. (Kyoto)5, 544 (1950)

    Google Scholar 

  5. Luttinger, J.M.: J. Math. Phys.4, 1154 (1963)

    Google Scholar 

  6. Mattis, D.C., Lieb, E.H.: J. Math. Phys.6, 304 (1965)

    Google Scholar 

  7. Araki, G., Murai, T.: Prog. Theor. Phys. (Kyoto)8, 639 (1952)

    Google Scholar 

  8. Edwards, S.F.: Proc. Phys. Soc.72, 685 (1958)

    Google Scholar 

  9. Murai, T.: Prog. Theor. Phys. (Kyoto)27, 899 (1962)

    Google Scholar 

  10. Mattis, D.C.: J. Math. Phys.15, 609 (1974)

    Google Scholar 

  11. Apostol, M.: Z. Phys. B-Condensed Matter22, 279 (1975)

    Google Scholar 

  12. Solyom, J.: Adv. Phys.28, 201 (1979)

    Google Scholar 

  13. Luther, A., Emery, V.J.: Phys. Rev. Lett.33, 589 (1974)

    Google Scholar 

  14. Emery, V.J., Luther, A., Peschel, I.: Phys. Rev. B13, 1272 (1976)

    Google Scholar 

  15. Lee, P.A.: Phys. Rev. Lett.34, 1247 (1975)

    Google Scholar 

  16. Chui, S.T., Lee, P.A.: Phys. Rev. Lett.35, 315 (1975)

    Google Scholar 

  17. Everts, H.U., Schulz, H.: Z. Phys. B-Condensed Matter22, 285 (1975)

    Google Scholar 

  18. Gutfreund, H., Klemm, R.A.: Phys. Rev. B14, 1073 (1976)

    Google Scholar 

  19. Schulz, H.: Z. Phys. B-Condensed Matter26, 377 (1977)

    Google Scholar 

  20. Ehrenreich, H., Cohen, M.H.: Phys. Rev.115, 786 (1959)

    Google Scholar 

  21. Williams, P.F., Bloch, A.N.: Phys. Rev. B10, 1097 (1974)

    Google Scholar 

  22. Giuliani, G., Tosatti, E., Tosi, M.P.: Lett. Nuovo Cimento16, 385 (1976)

    Google Scholar 

  23. Campos, V.B., Hipolito, O., Lobo, R.: Phys. Rev. B15, 4234 (1977); Phys. Status Solidi (b)81, 657 (1977)

    Google Scholar 

  24. Giuliani, G., Tosatti, E., Tosi, M.P.: J. Phys. C12, 2769 (1979)

    Google Scholar 

  25. Nobile, A., Tosi, M.P.: Nuovo Cimento51, 117 (1979)

    Google Scholar 

  26. Nobile, A., Tosatti, E.: J. Phys. C13, 589 (1980)

    Google Scholar 

  27. Friesen, W.I., Bergersen, B.: J. Phys. C13, 6627 (1980)

    Google Scholar 

  28. Pines, D.: Elementary Excitations in Solids. New York: Benjamin 1963

    Google Scholar 

  29. Bychkov, Y.A., Gorkov, L.P., Dzyaloshinsky, I.E.: Zh. Eksp. Teor. Fiz.50, 738 (1966) [Sov. Phys. JETP23, 489 (1966)]

    Google Scholar 

  30. Dzyaloshinsky, I.E., Kac, E.I.: Zh. Eksp. Teor. Fiz.55, 338 (1968);55, 2373 (1968)

    Google Scholar 

  31. Bhagavan, M.R.: J. Phys. C (Ser. 2)2, 1092 (1969)

    Google Scholar 

  32. Dzyaloshinsky, I.E., Larkin, A.I.: Zh. Eksp. Teor. Fiz.65, 411 (1973) [Sov. Phys. JETP38, 202 (1974)]

    Google Scholar 

  33. Menyhard, N., Solyom, J.: J. Low Temp. Phys.12, 529 (1973)

    Google Scholar 

  34. Solyom, J.: J. Low Temp. Phys.12, 547 (1973)

    Google Scholar 

  35. Galitskii, V., Migdal, A.: Zh. Eksp. Teor. Fiz.34, 139 (1958) [Sov. Phys. JETP7, 96 (1958)]

    Google Scholar 

  36. Gorkov, L.P.: Zh. Eksp. Teor. Fiz.34, 735 (1958) [Sov. Phys. JETP7, 505 (1958)]

    Google Scholar 

  37. Little, W.A.: Phys. Rev. A134, 1416 (1964)

    Google Scholar 

  38. Lieb, E.H., Wu, F.Y.: Phys. Rev. Lett.20, 1445 (1968)

    Google Scholar 

  39. Yang, C.N., Yang, C.P.: Phys. Rev.150, 327 (1966)

    Google Scholar 

  40. Gaudin, M.: Phys. Lett.24A, 55 (1967)

    Google Scholar 

  41. Takahashi, M.: Prog. Theor. Phys. (Kyoto)42, 1098 (1969)

    Google Scholar 

  42. Hubbard, J.: Proc. R. Soc. A276, 238 (1963); A277, 237 (1964)

    Google Scholar 

  43. Bloch, F.: Z. Phys.57, 545 (1929)

    Google Scholar 

  44. Wigner, E.P., Seitz, F.: Phys. Rev.43, 864 (1933);46, 509 (1934)

    Google Scholar 

  45. Wigner, E.P.: Phys. Rev.46, 1002 (1934)

    Google Scholar 

  46. Herring, C.: In: Magnetism. Rado, G.T., Suhl, H. (eds.). Vol. 4. New York: Academic Press 1966

    Google Scholar 

  47. Gray, A., Mathews, G.B.: A treatise on Bessel functions. New York: Dover 1966

    Google Scholar 

  48. See e.g. Roothaan, C.C.J.: Rev. Mod. Phys.23, 69 (1951)

    Google Scholar 

  49. Olszewski, S.: Acta Phys. Polon. A42, 265 (1972); Can. J. Phys.57, 243 (1979)

    Google Scholar 

  50. Overhauser, A.W.: Phys. Rev. Lett.4, 462 (1960)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physical Chemistry, Polish Academy of Sciences, 44/52 Kasprzaka, PL-01-224, Warszaw, Poland

    S. Olszewski

  2. International Centre for Theoretical Physics, Trieste, Italy

    S. Olszewski

Authors
  1. S. Olszewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Olszewski, S. Hartree-Fock approximation for the one-dimensional electron gas. Z. Physik B - Condensed Matter 45, 297–306 (1982). https://doi.org/10.1007/BF01321866

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01321866

Keywords

Search

Navigation