Static and dynamical properties of the polaronic state, formed on the surface of a liquid-helium film over different substrates, are studied from a hydrodynamical point of view. The formation of the dimple and the self-localization of electrons are studied through the self-consistent solution of the Schr\"odinger equation for an electron trapped to the dimple potential and the mechanical equilibrium equation for the helium surface. The mobility and the effective mass of the polaronic state are also calculated for different conditions accessible during an experiment. Existing results are reviewed and compared. Excellent agreement is found between calculated and experimental mobilities.
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Marques et al. (1989) studied this question.