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Inverse scattering on the line with incomplete scattering data

Tuncay Aktosun
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Abstract

The Schroedinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a corresponding reflection coefficient to the transmission coefficient. It is shown that there are a discrete number of potentials corresponding to the data and that their L^2-norms are related to each other in a simple manner. All those potentials are identified, and it is shown how an additional estimate on the L^2-norm in the data can uniquely identify the corresponding potential. The recovery is illustrated with some explicit examples.

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Tuncay Aktosun. 2004-02-10. Inverse scattering on the line with incomplete scattering data. https://arxiv.org/abs/math-ph/0402021

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