The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential

Roman G. Novikov

doi:10.1007/BF02101933

The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential

Roman G. Novikov

Université de Nantes
IEPT RAS

Research output: Contribution to journal › Article › peer-review

Abstract

The relations between the Faddeev functions and the functions of classical scattering theory are found in the complex domain at fixed energy. For the three-dimensional case (without assumption of "smallness" of the potential) it is proved that the exponentially decreasing potential is uniquely determined by its scattering amplitude at fixed energy.

Original language	English
Pages (from-to)	569-595
Number of pages	27
Journal	Communications in Mathematical Physics
Volume	161
Issue number	3
DOIs	https://doi.org/10.1007/BF02101933
Publication status	Published - 1 Apr 1994
Externally published	Yes

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AB - The relations between the Faddeev functions and the functions of classical scattering theory are found in the complex domain at fixed energy. For the three-dimensional case (without assumption of "smallness" of the potential) it is proved that the exponentially decreasing potential is uniquely determined by its scattering amplitude at fixed energy.

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The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential

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