Geodesic
Hydrogen atom as~indicator of~hidden symmetry of~a~ring-shaped potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 3, pp. 419-427

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The idea of an analogy between a ring-shaped potential and a Coulomb potential is advanced. It is shown that the expansion of the parabolic basis with respect to the spherical basis in the problem of a ring-shaped potential is determined by the Clebsch–Gordan coefficients of the group $SU(2)$ continued to the region of arbitrary real indices. The connection between these coefficients and the functions $_3F_2$ is found, and it is shown that they have a symmetry property under substitution of the parabolic quantum numbers. 
@article{TMF_1990_83_3_a9,
     author = {I. V. Lutsenko and G. S. Pogosyan and A. N. Sisakyan and V. M. Ter-Antonyan},
     title = {Hydrogen atom as~indicator of~hidden symmetry of~a~ring-shaped potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {419--427},
     publisher = {mathdoc},
     volume = {83},
     number = {3},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_83_3_a9/}
}
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I. V. Lutsenko; G. S. Pogosyan; A. N. Sisakyan; V. M. Ter-Antonyan. Hydrogen atom as~indicator of~hidden symmetry of~a~ring-shaped potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 3, pp. 419-427. http://geodesic.mathdoc.fr/item/TMF_1990_83_3_a9/