The energies of an electron above a liquid-helium surface are analyzed in terms of an electron-atom polarizability potential with an infinite barrier. An integration over a layer, and a summation over different layers, leads to a one-dimensional Coulomb potential with a 1/x² correction. This potential provides an accurate description of the observed one-dimensional Rydberg energies with a quantum defect.
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S. H. Patil (2001) studied this question.
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