Inverse scattering on the line with incomplete scattering data

Details Inverse scattering on the line with incomplete scattering data Inverse scattering on the line with incomplete scattering data

2004-02-10

arxiv.org/abs/math-ph/0402021v1

Contemporary Math. vol 362, AMS, Providence, 2004, pp. 1-11

Physics

Mathematical Physics

11 pages, to appear in Contemporary Mathematics

Scientific paper

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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