Inverse scattering at a fixed energy for discrere Schr\"{o}dinger operators on the square lattice

TL;DR

This paper demonstrates that for discrete Schrödinger operators on multi-dimensional square lattices with compact potentials, the potential can be uniquely reconstructed from the scattering matrix at a fixed energy, advancing inverse scattering theory.

Contribution

It establishes the uniqueness of potential reconstruction from fixed-energy scattering data for discrete Schrödinger operators on multi-dimensional lattices.

Findings

Potential is uniquely reconstructed from scattering matrix at fixed energy.

Addresses inverse scattering problem for discrete Schrödinger operators.

Extends inverse scattering theory to multi-dimensional lattice systems.

Abstract

We study an inverse scattering problem for the discrete Schr\"{o}dinger operator on the multi-dimensional square lattice, with compactly supported potential. We show that the potential is uniquely reconstructed from a scattering matrix for a fixed energy.