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arXiv · 1004.3641

Excited states of spherium

Pierre-François Loos·Peter M. W. Gill
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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 ($L\le3$) states. Kato cusp conditions and interdimensional degeneracies are discussed.

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Pierre-François Loos, Peter M. W. Gill. 2010-07-03. Excited states of spherium. https://doi.org/10.1080/00268976.2010.508472

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