Separability and the 3d Gelfand Levitan equation

Eric Kincanon

doi:10.14419/ijamr.v11i1.32034

Authors

Eric Kincanon
Gonzaga University

Received date: March 26, 2022

Accepted date: April 30, 2022

Published date: May 15, 2022

DOI:

https://doi.org/10.14419/ijamr.v11i1.32034

Keywords:

Inverse Scattering, Gelfand-Levitan Equation, Reflection Coefficient, One-Dimensional Scattering.

Abstract

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.
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References

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