Problems in inverse scattering of approximate reflection coefficient measurements

  • Authors

    • Eric Kincanon Gonzaga University
    2016-03-16
    https://doi.org/10.14419/ijamr.v5i2.5801
  • Ambiguities, Gelfand-Levitan, Inverse Scattering, Reflection Coefficient, Spectral Function

  • Abstract

    Because of the nonlinear nature of the Gelfand-Levitan equation, it may be a concern that a small difference in the reflection coefficient could lead to large changes in the corresponding potential. This paper considers this and shows that this need not be a concern. Though assumptions are made about the associated spectral measure function, these are not restrictive.

  • References

    1. [1] I.M. Gelfand, B.M. Levitan, on the determination of a differential equation by its spectral function, Dokl. Akad. Nauk. USSR 77 (1951) 557-560.

      [2] I.M. Gelfand, B.M. Levitan, on the determination of a differential equation by its spectral measure function, Izv. Akad. Nauk. SSR 15 (1951) 309-360.

      [3] K. Chadan, P.C. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer-Verlag, New York, 1977. http://dx.doi.org/10.1007/978-3-662-12125-2.

      [4] R. Jost, W. Kohn, on the relation between phase shift energy levels and the potential, Danske Vid. Selsk. Math. Fys. 27 (1953) 3-19.

      [5] E. Kincanon, an Orthogonal Set Composed from the Functionsenx, Applied Mathematics and Computation, 41, (1991) 69-75. http://dx.doi.org/10.1016/0096-3003(91)90107-X.

      [6] E. Kincanon, Approximate solution it the Gelfand-Levitan equation, Applied Mathematics and Computation, 53 (1993) 121-128. http://dx.doi.org/10.1016/0096-3003(93)90097-X.

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  • How to Cite

    Kincanon, E. (2016). Problems in inverse scattering of approximate reflection coefficient measurements. International Journal of Applied Mathematical Research, 5(2), 89-90. https://doi.org/10.14419/ijamr.v5i2.5801

    Received date: 2016-01-27

    Accepted date: 2016-03-13

    Published date: 2016-03-16