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arXiv · 1002.3400

Two electrons on a hypersphere: a quasi-exactly solvable model

Pierre-François Loos·Peter M. W. Gill
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Abstract

We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a $\mathcal{D}$-sphere ($\mathcal{D} \ge 1$), 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 $\mathcal{D}=3$ model bears the greatest similarity to normal physical systems.

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Pierre-François Loos, Peter M. W. Gill. 2010-02-17. Two electrons on a hypersphere: a quasi-exactly solvable model. https://doi.org/10.1103/physrevlett.103.123008

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