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Ukrainian Mathematical Journal

, Volume 52, Issue 5, pp 664–672 | Cite as

Approximation of general zero-range potentials

  • S. Albeverio
  • L. Nizhnik
Article

Abstract

A norm resolvent convergence result is proved for approximations of general Schrodinger operators with zero-range potentials. An approximation of the δ’-interaction by nonlocal non-Hermitian potentials (without a renormalization of the coupling constant) is also constructed.

Keywords

Point Interaction Oscillatory Potential Cauchy Data Oscillatory Function Oscillatory Characteristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. Albeverio, F. Gesztesy, R. Hoegh Krohn, and H. Holden, Solvable Models in Quantum Mechanics, Springer, New York 1988.MATHGoogle Scholar
  2. 2.
    S. Albeverio. F. Gesztesy, R. Hoegh Krohn, and W. Kirsch, “On point interactions in one dimension,” J. Operator Theory, 12, 101–126 (1984).MathSciNetGoogle Scholar
  3. 3.
    P. Seba, “The generalized point interaction in one dimension,” Czechoslovak. J. Phys., 36, 667–673 (1986).CrossRefMathSciNetGoogle Scholar
  4. 4.
    P. Seba, “A remark about the point interaction in one dimension,” Ann. Phys., 44, 323–328 (1987).MathSciNetGoogle Scholar
  5. 5.
    S. Albeverio, Z. Brzezniak, and L. Dabrowski, “Fundamental solution of the heat and Schrodinger equations with point interaction,” J. Fund. Anal., 128, 220–254 (1995).CrossRefMathSciNetGoogle Scholar
  6. 6.
    P. Seba, “Some remarks on the δ’-interaction in one dimension,” Rept. Math. Phys., 24, 111–120 (1986).MATHMathSciNetGoogle Scholar
  7. 7.
    P. R. Chernoff and R. J. Hughes, “A new class on point interaction in one dimension,” J. Fund. Anal., 111, 99–117 (1993).CrossRefMathSciNetGoogle Scholar
  8. 8.
    S. Albeverio, L. Dabrowski, and P. Kurasov, “Symmetries of Schrodinger operators with point interaction,” Lett. Math. Phys. 45, 33–47(1998).MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    S. Albeverio and V. Koshmanenko, Form-Sum Approximation of Singular Perturbation of Approximation of Self-Adjoint Operators, Preprint No. 771, BiBoS (1997).Google Scholar
  10. 10.
    T. Cheon and T. Shigehara, “Realizing discontinuous wave functions with renormalized short-range potentials,” Phys. Lett., 243, 111–116(1998).CrossRefGoogle Scholar
  11. 11.
    L.P. Nizhnik, “On point interaction in quantum mechanics,” Ukr. Mat. Zh., 49, No. 11, 1557–1560(1997).CrossRefMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • S. Albeverio
    • 1
  • L. Nizhnik
    • 2
  1. 1.Institut fur Angewandte MathematikUniversitat BonnGermany
  2. 2.Institute of MathematicsUkrainian Academy of SciencesKiev

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