Excited states of spherium

Details Excited states of spherium Excited states of spherium

2010-04-21

arxiv.org/abs/1004.3641v2

Mol. Phys. 108, 2527 (2010)

Physics

Condensed Matter

Other Condensed Matter

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

Scientific paper

10.1080/00268976.2010.508472

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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