Skip to main content
SpringerLink
Log in

Analytic conditions for the existence of localized electron states in a linear chain with an arbitrary number of impurities

  • Published:
Czechoslovak Journal of Physics B Aims and scope

Abstract

The effective Hamiltonian and the negative eigenvalue theorem are used to obtain an analytic formula for the integrated density of electron states in a linear chain with an arbitrary number of impurities within the tight binding approximation. From this formula, the analytic conditions for the existence of localized electron states lying above or below the band of states of host atoms are obtained. The way of obtaining the energies of localized states and the form of eigenvectors are also discussed.

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. Skála L., Czech. J. Phys.B 26 (1976), 199.

    Google Scholar 

  2. Goodwin E. T., Proc. Cambr. Phil. Soc.35 (1939), 221.

    Google Scholar 

  3. Puszkarski H., Surf. Sci.34 (1973), 125.

    Google Scholar 

  4. Löwdin P. O., J. Appl. Phys. Suppl.33 (1962), 251.

    Google Scholar 

  5. Micha D. A.,in Advances in Quantum Chemistry Vol. 8, Academic Press, New York and London 1974.

    Google Scholar 

  6. Levy H., Lessman F., Finite Difference Equations, Sir Isaac Pitman and Sons, Ltd., London 1959.

    Google Scholar 

  7. Marcus M., Minc H., A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon Inc., Boston 1964.

    Google Scholar 

  8. Dean P., Rev. Mod. Phys.44 (1972), 127.

    Google Scholar 

  9. Jeffreys H., Jeffreys B. S., Methods of Mathematical Physics, At the University Press, Cambridge 1946, p. 127.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Prague, Ke Karlovu 3, 121 16, Praha 2, Czechoslovakia

    L. Skála

Authors
  1. L. Skála
    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

Skála, L. Analytic conditions for the existence of localized electron states in a linear chain with an arbitrary number of impurities. Czech J Phys 27, 1152–1160 (1977). https://doi.org/10.1007/BF01589006

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01589006

Keywords

Search

Navigation