Geodesic
Energy spectrum in the force field of an electrostatic image
Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 1, pp. 109-115 
O. F. Dorofeev; B. A. Lysov; O. S. Pavlova; I. M. Ternov. Energy spectrum in the force field of an electrostatic image. Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 1, pp. 109-115. http://geodesic.mathdoc.fr/item/TMF_1989_78_1_a9/
@article{TMF_1989_78_1_a9,
     author = {O. F. Dorofeev and B. A. Lysov and O. S. Pavlova and I. M. Ternov},
     title = {Energy spectrum in~the force field of~an~electrostatic image},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {109--115},
     year = {1989},
     volume = {78},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_78_1_a9/}
}
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JO  - Teoretičeskaâ i matematičeskaâ fizika
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%A B. A. Lysov
%A O. S. Pavlova
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%J Teoretičeskaâ i matematičeskaâ fizika
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new model is suggested for describing localized electronic states in the vicinity of the surface of liquid helium. The model exploits nonuniqueness of self-adjoint extensions of the hamiltonian for an electron moving in an electrostatic image-induced potential near the flat interface isolator–vacuum. Unlike the Grimes model, the model proposed has only one phenomenological parameter, the mixing angle. It is shown that a proper choice of the mixing angle makes it possible to present the complete explanation of spectroscopic data on electrical dipole transitions between one-particle electronic states localized above the surface of liquid $^4\mathrm{He}$ or $^3\mathrm{He}$.

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