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Potential splitting and numerical solution of the inverse scattering problem on the line. (English) Zbl 1054.34137

A numerical method is suggested for the solution of the inverse scattering problem for the Sturm-Liouville equation \(-y''+V(x)y=\lambda y\) on the line, where the potential \(V(x)\) is real-valued, integrable, has a finite first moment, and contains no bound states.

MSC:

34L25 Scattering theory, inverse scattering involving ordinary differential operators
65L09 Numerical solution of inverse problems involving ordinary differential equations
34B24 Sturm-Liouville theory
47E05 General theory of ordinary differential operators
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