Letters in Mathematical Physics

, Volume 85, Issue 2–3, pp 129–133 | Cite as

On the Number of Negative Eigenvalues of a Schrödinger Operator with Point Interactions

Article

Abstract

We give a sufficient condition for a one-dimensional Schrödinger operator with point δ-interactions, which contain m points of interaction with negative intensities, to have at least m negative eigenvalues.

Mathematics Subject Classification (2000)

47A10 34L40 

Keywords

number of negative eigenvalues point interactions Schrödinger operators. 

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References

  1. 1.
    Albeverio S., Nizhnik L.: Schrödinger operators with anumber of negative eigenvalues equal to the number of point interactions. Methods Funct. Anal. Topol. 9(4), 273–286 (2003)MATHMathSciNetGoogle Scholar
  2. 2.
    Albeverio S., Nizhnik L.: On the number of negative eigenvalues of a one-dimensional Schrödinger operator with point interactions. Lett. Math. Phys. 65, 27–35 (2003)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Albeverio S., Gesztesy F., Hoegh-Krohn R., Holden H.: Solvable Models in Quantum Mechanics. Springer, Heidelberg (1988)MATHGoogle Scholar
  4. 4.
    Chatelin F.: Valeurs Propres de Matrices. Masson, Paris (1988)MATHGoogle Scholar
  5. 5.
    Kato T.: Perturbation Theory for Linear Operators. Springer, Heidelberg (1966)MATHGoogle Scholar
  6. 6.
    Kato T.: Short Introduction to Perturbation Theory for Linear Operators. Springer, Heidelberg (1982)MATHGoogle Scholar
  7. 7.
    Varga R.S.: Geršgorin and his circles. Springer Series in Computational Mathematics. Springer, Berlin (2004)Google Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Division of Mathematical and Physical Sciences, Graduate School of Natural Science and TechnologyKanazawa UniversityKanazawaJapan

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