Skip to main content
SpringerLink
Log in

Spectral and scattering theory of Schrödinger operators related to the stark effect

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

Abstract

We analyze the spectral properties and discuss the scattering theory of operators of the formH=H 0+V,H 0=−Δ+E·x. Among our results are the existence of wave operators, Ω±(H, H 0), the nonexistence of bound states, and a (speculative) description of resonances for certain classes of potentials.

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. Agmon, S.: Proceedings of the Tokyo Int. Conf. on Functional Analysis and Related Topics, 1969

  2. Agmon, S.: J. d'Analyse, Math.23, 1–25 (1970)

    Google Scholar 

  3. Aronszajn, N.: J. Math. Pures Appl.36, 235–249 (1957)

    Google Scholar 

  4. Balslev, E., Combes, J.M.: Commun. math. Phys.22, 280–294 (1971)

    Google Scholar 

  5. Chandler, C., Stapp, H.: J. Math. Phys.10, 826–859 (1969)

    Google Scholar 

  6. Condon, E.U., Shortley, G.H.: The theory of atomic spectra. Cambridge: Cambridge University Press 1970

    Google Scholar 

  7. Dunford, N., Schwartz, J.T.: Linear operators, Vol. II. New York: Interscience 1958

    Google Scholar 

  8. Herbst, I.: Commun. math. Phys.35, 193–214 (1974)

    Google Scholar 

  9. Jansen, K.H., Kalf, H.: Comm. Pure Appl. Math.28, 747–752 (1975)

    Google Scholar 

  10. Kato, T.: Trans. Am. Math. Soc.70, 195–211 (1951)

    Google Scholar 

  11. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Spriner 1966

    Google Scholar 

  12. Kato, T.: Comm. Pure Appl. Math.12, 403–425 (1959)

    Google Scholar 

  13. Landau, L.D., Lifshitz, E.M.: Quantum mechanics. Oxford: Pergamon 1954

    Google Scholar 

  14. Lavine, R.: Commun. math. Phys.20, 301–323 (1971)

    Google Scholar 

  15. Lieb, E.H., Simon, B., Wightman, A.S.: Studies in mathematical physics, essays in honor of V. Bargmann. Princeton: Princeton University Press 1976

    Google Scholar 

  16. Rauch, J., Reed, M.: Commun. math. Phys.29, 105–111 (1973)

    Google Scholar 

  17. Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. I, II, New York-London: Academic Press 1974, 1975

    Google Scholar 

  18. Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. III, to appear

  19. Ruelle, D.: Helv. Phys. Acta35, 147 (1962)

    Google Scholar 

  20. Simon, B.: Comm. Pure. Appl. Math.22, 531–538 (1969)

    Google Scholar 

  21. Simon, B.: Ann. Math.97, 247–274 (1973)

    Google Scholar 

  22. Simon, B.: Commun. math. Phys.23 37 (1971)

    Google Scholar 

  23. Titchmarsh, E.C.: Eigenfunction expansions associated with second order differential equations. Oxford: Oxford University Press 1958

    Google Scholar 

  24. Weidmann, J.: Bull. AMS73, 452–456 (1967)

    Google Scholar 

  25. Wilcox, C.H.: Perturbation Theory and Its Application in Quantum Mechanics. New York-London: J. Wiley 1966

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Joseph Henry Laboratories of Physics, Princeton University, 08540, Princeton, New Jersey, USA

    J. E. Avron (Wigner Fund Fellow) & I. W. Herbst

  2. Technische University of Berlin, Germany

    J. E. Avron (Wigner Fund Fellow)

Authors
  1. J. E. Avron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. W. Herbst
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by W. Hunziker

Supported in part by NSF Grant MPS 74-22844

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avron, J.E., Herbst, I.W. Spectral and scattering theory of Schrödinger operators related to the stark effect. Commun.Math. Phys. 52, 239–254 (1977). https://doi.org/10.1007/BF01609485

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01609485

Keywords

Search

Navigation