Existence of propagators for time-dependent Coulomb-like potentials

Abstract

We prove existence of propagators for a time-dependent Schrodinger equation with a new class of softened Coulomb potentials, which we allow to be time dependent, in the context of time-dependent density functional theory. We compute explicitly the Fourier transform of these new potentials, and provide an alternative proof for the Fourier transform of the Coulomb potential using distribution theory. Finally, we show the new potentials are dilatation analytic, and discuss various properties and applications related to the essential spectrum of the Hamiltonian associated to these potentials.