Construction of a two-dimensional Schrödinger operator with given scattering amplitude at fixed energy
The inverse scattering problem for the two-dimensional Schrödinger operator \(H=-\Delta +V(x,y)\) is considered. It is shown that the classical necessary properties of the scattering amplitude (duality and unitarity) are sufficient conditions for the existence of a decreasing potential with given scattering amplitude at fixed energy, if the \(L^ 2\) norm of the amplitude is small.
scientific article; zbMATH DE number 3996215