Image-potential states on dielectric-covered metal surfaces: Variational versus numerical approach

We find a set of simple variational hydrogeniclike wave functions for the three lowest image-potential states of electrons trapped on dielectric layers supported by a metallic substrate. We calculate the variational parameters and find excellent agreement with the numerical calculations, both for eigenenergies and eigenfunctions. A simple form of the wave functions and their accuracy enable analytical formulation and treatment of many-body processes in these quasi-two-dimensional electronic systems.