Abstract
As an approach to the highly excited states of a Coulomb three-body system, a Schrödinger operator on a hypersphere of radius ρ, the hyperradius of the system, is considered. A corresponding spectral problem is studied in the limit ρ→∞, which is interpreted as semiclassical. For two particular models, the semiclassical quantization rules for eigenvalues along with the WKB-type approximations for eigenfunctions are obtained. One of the models imitates a heliumlike atom in the Wannier region.
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