Quantum inverse scattering for time-dependent repulsive Hamiltonians

Abstract: We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonian. The time-dependent coefficient on the repulsive term decays as the inverse square of time, which is the threshold between the standard free Schroedinger operator and the time-independent repulsive Hamiltonian. Applying the Enss-Weder time-dependent method, we can determine uniquely the short-range potential functions with Coulomb-like singularities from the velocity limit of the scattering operator.