Scattering of quantum wave packets by shallow potential islands: A quantum lens

Abstract: We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equation as for refracted rays in classical optics.