Excited states of spherium

Abstract

We report analytic solutions of a recently discovered quasi-exactly solvable model consisting of two electrons, interacting {\em via} a Coulomb potential, but restricted to remain on the surface of a $\mathcal{D}$-dimensional sphere. Polynomial solutions are found for the ground state, and for some higher ($L\le 3$) states. Kato cusp conditions and interdimensional degeneracies are discussed.

6 pages, 2 figures, to appear in Mol. Phys

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