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Stability of the inverse problem for the radial schrödinger equation with an increasing potential

Abstract

It is shown that a potential reconstructed from a spectral function is stable with respect to an error in the determination of the spectral function at finite energies. The absence of spectral data at high energies leads to the consequence that at finite distances the term in the potential, averaged over the spatial period of the Compton wave length, is stable.

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Literature cited

  1. 1.

    V. A. Marchenko, Spectral Theory of Sturm-Liouville Operators [in Russian], Naukova Dumka, Kiev (1972).

  2. 2.

    K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer-Verlag, New York (1977).

  3. 3.

    H. Grosse and A. Martin, Phys. Reports,60, No. 6, 341 (1980).

  4. 4.

    B. McWilliams, Phys. Rev.,D20, No. 5, 1221 (1979).

  5. 5.

    M. N. Adamyan, Teor. Mat. Fiz.,48, No. 1, 70 (1981).

  6. 6.

    V. B. Gostev, V. S. Mineev, and A. R. Frenkin, Dokl. Akad. Nauk SSSR,262, No. 6, 1364 (1982).

  7. 7.

    A. G. Kostyuchenko and I. S. Sargsyan, Eigenvalue Distributions [in Russian], Nauka, Moscow (1979).

  8. 8.

    B. M. Levitan, Izv. Akad. Nauk SSSR, Ser. Mat.,19, 33 (1955).

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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 45–49, March, 1987.

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Adamyan, M.N. Stability of the inverse problem for the radial schrödinger equation with an increasing potential. Soviet Physics Journal 30, 220–223 (1987). https://doi.org/10.1007/BF00897859

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Keywords

  • Inverse Problem
  • Spectral Data
  • Wave Length
  • Spectral Function
  • Spatial Period