Separability and the 3d Gelfand Levitan equation

  • Authors

    • Eric Kincanon Gonzaga University
    2022-05-15
    https://doi.org/10.14419/ijamr.v11i1.32034
  • Inverse Scattering, Gelfand-Levitan Equation, Reflection Coefficient, One-Dimensional Scattering.

  • The 1D Gelfand-Levitan equation has been well studied with respect to the separability of the spectral measure function. The analytic solu-tion has been shown to be associated with reflectionless potentials. This paper considers the 3D version of this equation to see if an analytic solution can be found for a separable spectral measure function and if it also corresponds to known reflectionless potentials. Though the analytic solution is shown, it does not correspond to reflectionless potentials.

     

     

  • References

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      [5] Spectral Measure Function Separability and Reflectionless Potentials,†Eric Kincanon, Applied Mathematics and Computation, Vol 123, No 3, 409-412. https://doi.org/10.1016/S0096-3003(00)00086-2.

      [6] A Method to Construct Reflectionless Potentials,†Eric Kincanon, Vol 165, No 3, 565-569, Applied Mathematics and Computation, (June 2005). https://doi.org/10.1016/j.amc.2004.04.075.

      [7] Error Propagation in the Gel’Fand Levitan Equation,†Eric Kincanon, Vol 182, No 2, 1639-1641, Applied Mathematics and Computation, (November 2006). https://doi.org/10.1016/j.amc.2006.06.001.

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      [9] I. Kay, H. E. Moses, A simple verification of the Gelfand-Levitan equation for the three-dimensional problem, Comm on Pure and Applied Mathematics, 14 (1961) 435-445. https://doi.org/10.1002/cpa.3160140319.

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  • How to Cite

    Kincanon, E. (2022). Separability and the 3d Gelfand Levitan equation. International Journal of Applied Mathematical Research, 11(1), 11-13. https://doi.org/10.14419/ijamr.v11i1.32034