SEMICLASSICAL QUANTIZATION FOR COULOMB-SYSTEMS ON A HYPERSPHERE

As an approach to the highly excited states of a Coulomb three-body system, a Schrodinger operator on a hypersphere of radius-rho, the hyperradius of the system, is considered. A corresponding spectral problem is studied in the limit-rho --> infinity, 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.