Alternative form of the Gelfand Levitan equation

  • Authors

    • Eric Kincanon Gonzaga University
    2021-12-01
    https://doi.org/10.14419/ijamr.v10i2.31842
  • Inverse Scattering, Gelfand-Levitan Equation, Reflection Coefficient, One-Dimensional Scattering.

  • Abstract

    This paper presents an alternative form of the Gelfand-Levitan Equation. By assuming a particular form of the spectral measure function and the potential kernel, an equation relating the potential and the reflection coefficient is found. This equation has an advantage over the Gelfand-Levitan Equation in that it can be solved without using iterative methods. The validity of the equation is demonstrated by looking at a singular and non-singular potential.

     

     

  • 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. https://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.

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  • How to Cite

    Kincanon, E. (2021). Alternative form of the Gelfand Levitan equation. International Journal of Applied Mathematical Research, 10(2), 28-31. https://doi.org/10.14419/ijamr.v10i2.31842

    Received date: 2021-10-22

    Accepted date: 2021-11-20

    Published date: 2021-12-01