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

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

2010-02-17

arxiv.org/abs/1002.3400v1

Phys. Rev. Lett. 103, 123008 (2009)

Physics

Condensed Matter

Other Condensed Matter

4 pages, 0 figure

Scientific paper

10.1103/PhysRevLett.103.123008

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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