On inverse scattering problem for the Schrödinger equation with repulsive potentials

We study multidimensional inverse scattering for Hamiltonians with repulsive potentials. Assuming short-range conditions for the interaction potential, the high velocity limit of the scattering operator determines uniquely the short-range part, using the Enss-Weder time-dependent method (1995). This work improves on a previous result obtained by Nicoleau (2006). We can allow interaction potentials to have not only slower decays but also Coulomb-like singularities.