Inverse scattering for a Schrödinger operator with a repulsive potential (Q2505399)

The author considers the inverse scattering problem for the Schrödinger operator \(-\Delta-x\cdot x+V(x),\) where \(x\in\mathbb {R}^n\) and \(V\) is a repulsive potential decaying at infinity and satisfying certain other restrictions. It is shown that \(V\) is uniquely determined by the high energy limit of the scattering operator.