ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045

Complete solution of the Marchenko equation for a simple model system; pp. 267–283

Full article in PDF format | doi: 10.3176/proc.2016.3.07

Author
Matti Selg

Abstract

An example of full solution of the inverse scattering problem on the half line (from 0 to ∞) 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 shift is derived.


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