Skip to main content
SpringerLink
Log in

Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials

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

Abstract

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.

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. Abramov A.A., Aslanyan A., Davies E.B. (2001) Bounds on complex eigenvalues and resonances. J. Phys. A 34, 57–72

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Davies E.B., Nath J. (2002) Schrödinger operators with slowly decaying potentials. J. Comput. Appl. Math. 148(1): 1–28

    Article  MATH  MathSciNet  Google Scholar 

  3. Aizenman M., Lieb E.H. (1978) On semi-classical bounds for eigenvalues of Schrödinger operators. Phys. Lett. 66A, 427–429

    MathSciNet  Google Scholar 

  4. Laptev, A., Weidl, T.: Recent results on Lieb–Thirring inequalities, Journées “Équations aux Dérivées Partielles” (La Chapelle sur Erdre, 2000), Exp. No. XX, University of Nantes, Nantes (2000)

  5. Lieb E.H., Thirring W.: In: Lieb, E., Simon, B., Wightman, A. (eds.) Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities, in Studies in Mathematical Physics. pp. 269–303 Princeton University Press, Princeton, (1976)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Rupert L. Frank & Ari Laptev

  2. Department of Physics, Princeton University, P. O. Box 708, Princeton, NJ, 08544, USA

    Elliott H. Lieb & Robert Seiringer

  3. Department of Mathematics, Princeton University, P. O. Box 708, Princeton, NJ, 08544, USA

    Elliott H. Lieb

Authors
  1. Rupert L. Frank
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ari Laptev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elliott H. Lieb
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Robert Seiringer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elliott H. Lieb.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frank, R.L., Laptev, A., Lieb, E.H. et al. Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials. Lett Math Phys 77, 309–316 (2006). https://doi.org/10.1007/s11005-006-0095-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-006-0095-1

Mathematics Subject Classification

Keywords

Search

Navigation