Problems in inverse scattering of approximate reflection coefficient measurements

 
 
 
  • Abstract
  • Keywords
  • References
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  • 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.


  • Keywords


    Ambiguities; Gelfand-Levitan; Inverse Scattering; Reflection Coefficient; Spectral Function

  • References


      [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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Article ID: 5801
 
DOI: 10.14419/ijamr.v5i2.5801




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