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

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

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