In this paper we prove that the Cauchy data for the Schrödinger equation in the two-dimensional case determines a potential from *L _{p}
* (for

*p*> 2) uniquely. We also obtain a linear inversion formula for smooth potentials.

Show Summary Details# Recovering a potential from Cauchy data in the two-dimensional case

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A. L. Bukhgeim

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Get Access to Full TextIn this paper we prove that the Cauchy data for the Schrödinger equation in the two-dimensional case determines a potential from *L _{p}
* (for

Keywords: Riemann–Hilbert problem; potential; Schrödinger equation; inversion formula; Cauchy data

**Received**: 2007-06-14

**Revised**: 2007-11-24

**Published Online**: 2008-03-05

**Published in Print**: 2008-01-01

**Citation Information: **Journal of Inverse and Ill-posed Problems jiip, Volume 16, Issue 1, Pages 19–33, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2008.002.

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