Stability estimate in the inverse scattering for a single quantum particle in an external short-range potential

Mourad Bellassoued; Luc Robbiano

doi:10.1016/j.crma.2019.09.009

Partial differential equations

Stability estimate in the inverse scattering for a single quantum particle in an external short-range potential
[Estimation de stabilité en diffusion inverse pour une particule quantique en présence d'un potentiel à courte portée]

Présenté par : the Editorial Board

Mourad Bellassoued ¹ ; Luc Robbiano ²

¹ Université de Tunis El Manar, École nationale d'ingénieurs de Tunis, LAMSIN, B.P. 37, 1002 Tunis, Tunisia
² Laboratoire de mathématiques, Université de Versailles – Saint-Quentin-en-Yvelines, 78035 Versailles, France

Comptes Rendus. Mathématique, Volume 357 (2019) no. 10, pp. 784-798.

Résumé
Abstract

Dans cet article, nous considérons le problème de la diffusion inverse pour l'opérateur de Schrödinger avec un potentiel électrique à courte portée. Nous prouvons en dimension $n \geq 2$ que la connaissance de l'opérateur de diffusion détermine le potentiel électrique et nous établissons une estimation de stabilité de type Hölder pour la détermination du potentiel électrique à courte portée.

In this paper we consider the inverse scattering problem for the Schrödinger operator with short-range electric potential. We prove in dimension $n \geq 2$ that the knowledge of the scattering operator determines the electric potential and we establish Hölder-type stability in determining the short range electric potential.

Reçu le : 2018-09-04
Accepté le : 2019-09-16
Publié le : 2019-10-01

DOI : 10.1016/j.crma.2019.09.009

Affiliations des auteurs :

Mourad Bellassoued ¹ ; Luc Robbiano ²

¹ Université de Tunis El Manar, École nationale d'ingénieurs de Tunis, LAMSIN, B.P. 37, 1002 Tunis, Tunisia
² Laboratoire de mathématiques, Université de Versailles – Saint-Quentin-en-Yvelines, 78035 Versailles, France

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     title = {Stability estimate in the inverse scattering for a single quantum particle in an external short-range potential},
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Mourad Bellassoued; Luc Robbiano. Stability estimate in the inverse scattering for a single quantum particle in an external short-range potential. Comptes Rendus. Mathématique, Volume 357 (2019) no. 10, pp. 784-798. doi : 10.1016/j.crma.2019.09.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.09.009/

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