Complete solution of the Marchenko equation for a simple model system

Proceedings of the Estonian Academy of Sciences

Matti Selg¹ 

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关键词: inverse scattering;    Marchenko equation;    Levinson theorem;    Riemann–Siegel function;   

DOI  :  10.3176/proc.2016.3.07

学科分类：化学（综合）

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

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.

【 授权许可】

Unknown