Fixed energy inverse problem for exponentially decreasing potentials

Details Fixed energy inverse problem for exponentially decreasing potentials Fixed energy inverse problem for exponentially decreasing potentials

2003-07-17

arxiv.org/abs/math/0307253v1

Methods and Applications of Analysis 9:239-248 (2002)

Mathematics

Analysis of PDEs

Addendum added, on July 17, 2003, to the published version

Scientific paper

In this paper we show that in two-body scattering the scattering matrix at a fixed energy determines real-valued exponentially decreasing potentials. This result has been proved by Novikov previously, see also the work of Novikov and Khenkin using a d-bar-equation. We present a different method, which combines a density argument and real analyticity in part of the complex momentum. The latter has been noted by Novikov and Khenkin; here we give a short proof using contour deformations. In the addendum to the paper we also supply a reference to the work of Eskin and Ralston that did not appear in the published paper since we were unaware of the relevant aspects of their work.

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