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On inverse scattering at a fixed energy for potentials with a regular behaviour at infinity*

Ricardo Weder1 and Dimitri Yafaev2

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We study the inverse scattering problem for electric potentials and magnetic fields in {\bb R}^d, d\geq 3 , that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.


Footnote
*  Research partially supported by Universidad Nacional Autónoma de México under project PAPIIT-DGAPA IN 105799, by CONACYT under project P42553F and by the European Group of Research SPECT.
PACS

03.65.Nk Scattering theory

02.30.Zz Inverse problems

02.10.Yn Matrix theory

MSC

81U20 S-matrix theory, etc.

47A40 Scattering theory (See also 34L25, 35P25, 81Uxx)

81U40 Inverse scattering problems

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 6 (December 2005)

Received 9 August 2005, in final form 23 September 2005

Published 14 October 2005



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