Abstract
We generalize the Hilleraas equation (in momentum space) to six dimensions for hydrogenic atoms. This leads to Laplace's equation on a five-dimensional hypersphere in the six-dimensional Euclidean manifold. It is shown that an additional quantum number can be identified with the charge of the nucleus. The energy levels of the atom are degenerate with respect to the additional quantum number and also with respect to the azimuthal and magnetic quantum numbers in the Fock-Hilleraas problem.
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Translated from Izvestiya Vysshikh, Uchebykh Zavedenii, Fizika, No. 4, pp. 66–69, April 1985.
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Vladimirov, Y.S., Kislov, V.V. Charge of the nucleus of a hydrogenic atom as the eigenvalue of a six-dimensional wave equation in momentum space. Soviet Physics Journal 28, 313–316 (1985). https://doi.org/10.1007/BF01301562
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DOI: https://doi.org/10.1007/BF01301562