Abstract
We calculate the ground and the first excited states of an electron
trapped within a dimple on a thin liquid helium film. The electron is
localized by a positive impurity charge which is located on the
substrate supporting the film. The mechanical equilibrium equation for
the liquid helium surface is coupled to the Schrodinger equation which
are solved using a variational approach. The energies of the ground and
first excited states are obtained as a function of the helium film
thickness and external electrical, and magnetic fields which are
directly perpendicular to the two-dimensional system.
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