Complete solution of the Marchenko equation for a simple model system

An example of full solution of the inverse scattering problem on the half line (from 0 to infinity ) is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a real potential. First one calculates all...

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Bibliographic Details
Published in:Proceedings of the Estonian Academy of Sciences 2016-01, Vol.65 (3), p.267-267
Main Author: Selg, Matti
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Integral equations
Inverse scattering
Mathematical analysis
Mathematical models
Morse potential
Spectra
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Summary:An example of full solution of the inverse scattering problem on the half line (from 0 to infinity ) is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a real potential. First one calculates all spectral characteristics for the fixed model system. This way one gets all the necessary input data (otherwise unobtainable) to implement powerful methods of the inverse scattering theory. In this paper, the multi-step procedure to solve the Marchenko integral equation is described in full detail. Several important analytic properties of the Morse potential are unveiled. For example, a simple analytic algorithm to calculate the phase shiftis derived.
ISSN:1736-6046
1736-7530
DOI:10.3176/proc.2016.3.07