We consider the problem of finding the energy spectrum of electrons localized above the surface of a liquid helium film under the electrostatic attraction of induced charges. We show that the forces of attraction to the charges induced on the surface of a conductor located beneath the film begin to additionally influence the forces of attraction of the electrons to the free liquid surface as the film thickness decreases. When the film thickness becomes less than 10 |ìm, this influence causes a significant increase in the energy difference between the lower levels and a decrease in their depth. We suggest a numerical method for solving the problem and present the results of our calculations of the energy spectrum of electrons localized above the surfaces of liquid ~3He, ~4He, and neon films. The influence of the pressing electric field on the energy spectrum is considered.
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