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

Abstract

The energies of 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 for 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.