Inverse scattering at a fixed energy for long-range potentials

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February 2007, 1(1): 217-224. doi: 10.3934/ipi.2007.1.217

Inverse scattering at a fixed energy for long-range potentials

Ricardo Weder ^1, and Dimitri Yafaev ^2,

1.	Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-726, México DF 01000, United States
2.	IRMAR, Université de Rennes I., Campus de Beaulieu, 35042 Rennes, Cedex, France

Received September 2006 Published January 2007

Abstract
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In this paper we consider the inverse scattering problem at a fixed energy for the Schrödinger equation with a long-range potential in $R^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading forward singularity of the scattering amplitude at some positive energy.

Keywords: fixed energy., inverse scattering, long-range potentials.

Mathematics Subject Classification: Primary: 81U40, 35P25, 35Q40, 35R3.

Citation: Ricardo Weder, Dimitri Yafaev. Inverse scattering at a fixed energy for long-range potentials. Inverse Problems & Imaging, 2007, 1 (1) : 217-224. doi: 10.3934/ipi.2007.1.217

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