Abstract
An electron on the surface of a liquid-helium film in a uniform magnetic field is studied as a polaron problem by an extended variational scheme of the Lee-Low-Pines theory. To describe the electron motion we employ a model, used in the path-integral formalism, in which an electron is coupled to a fictitious particle by a spring. The ground-state energy is obtained for the limiting values of the magnetic field strength and the electron-surface (ripplon) coupling constant. We find that the polaron can assume three kinds of states for the limiting cases: a free state, a self-trapped state, and a magnetically trapped state.
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