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

Isozaki, Hiroshi; Morioka, Hisashi

Annales de l'Institut Fourier, Tome 65 (2015) no. 3, pp. 1153-1200.

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.

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.

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