Variational approach to the problem of the energy spectrum of surface electrons over a liquid helium film

Abstract

The energies of the first two subbands are calculated, within a variational approach, for electrons localized over the surface of a liquid helium film covering a solid substrate. The results are obtained for arbitrary value of the dielectric constant of the solid substrate, covering both the limit of a substrate with a dielectric constant close to unity (such as a rare gas solid) and a metal. The results for the subband energies in the case of a metallic substrate are compared with those obtained previously by a different method by Gabovich, Ilchenko, and Pashitskii. The agreement is rather good, supporting the applicability of the variational method for calculating the energy spectrum of surface electrons in a wide range of substrate parameters.