Two electrons on a hypersphere: A quasiexactly solvable model

We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a D-sphere (D≥1), is a polynomial in the interelectronic distance u for a countably infinite set of values of the radius R. A selection of these radii and the associated energies are reported for ground and excited states on the singlet and triplet manifolds. We conclude that the D=3 model bears the greatest similarity to normal physical systems.