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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 108, 2010 - Issue 19-20: Proceedings of Molecular Quantum Mechanics 2010: An International Conference in Honour of Professor Henry F. Schaefer III
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Invited Articles

Excited states of spherium

Pierre-François Loos Research School of Chemistry, Australian National University, Australian Capital Territory 0200, Canberra, Australia
&
Peter M.W. Gill Research School of Chemistry, Australian National University, Australian Capital Territory 0200, Canberra, AustraliaCorrespondence[email protected]
Pages 2527-2532 | Received 21 Apr 2010, Accepted 08 Jul 2010, Published online: 02 Sep 2010
 
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Abstract

We report analytic solutions of a recently discovered quasi-exactly solvable model consisting of two electrons, interacting via a Coulomb potential, but restricted to remain on the surface of a 𝒟-dimensional sphere. Polynomial solutions are found for the ground state, and for some higher (L ≤ 3) states. Kato cusp conditions and interdimensional degeneracies are discussed.

Acknowledgements

PMWG thanks the NCI National Facility for a generous grant of supercomputer time and the Australian Research Council (Grant DP0984806) for funding.

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