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

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 n2 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 n2 that the knowledge of the scattering operator determines the electric potential and we establish Hölder-type stability in determining the short range electric potential.

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DOI : 10.1016/j.crma.2019.09.009

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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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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