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

References in corpus (6)

• Two electrons on a hypersphere: a quasi-exactly solvable model
• Ground state of two electrons on a sphere
• Correlation energy of two electrons in the high-density limit
• Hooke's law correlation in two-electron systems
• Correlation energy of two electrons in a ball
• Ground state of two electrons on concentric spheres