Inverse scattering at a fixed energy for Discrete Schrödinger Operators on the square lattice

[Diffusion inverse à énergie fixée pour l’opérateur Schrödinger sur un réseau carré]

Isozaki, Hiroshi ; Morioka, Hisashi

Annales de l'Institut Fourier, Tome 65 (2015), p. 1153-1200 / Harvested from Numdam

Résumé

Nous étudions un problème inverse de diffusion pour l’opérateur de Schrödinger discret sur un réseau carré ${\mathbb{Z}}^d$, $d \ge 2$, avec un potentiel à support compact. Nous montrons que le potentiel est uniquement determiné en utilisant la matrice de diffusion à énergie fixée.

Abstract

We study an inverse scattering problem for the discrete Schrödinger operator on the square lattice ${\mathbb{Z}}^d$, $d \ge 2$, with compactly supported potential. We show that the potential is uniquely reconstructed from a scattering matrix for a fixed energy.

Détail

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/aif.2954
Classification:  81U40,  47A40,  39A12
Mots clés: l’opérateur de Schrödinger, la théorie de diffusion, le problème inverse

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