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

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.

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References

  1. 1.

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

    MATH  Article  ADS  MathSciNet  Google Scholar 

  2. 2.

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

    MATH  Article  MathSciNet  Google Scholar 

  3. 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. 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. 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)

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Correspondence to Elliott H. Lieb.

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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

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Mathematics Subject Classification

  • Primary, 35P15
  • Secondary, 81Q10

Keywords

  • Schrödinger operator
  • Lieb–Thirring inequalities
  • complex potential