Two electrons in an external oscillator potential: hidden algebraic structure

Details Two electrons in an external oscillator potential: hidden algebraic structure Two electrons in an external oscillator potential: hidden algebraic structure

1994-06-03

arxiv.org/abs/hep-th/9406018v1

Phys.Rev.A50:5335-5337,1994

Physics

High Energy Physics

High Energy Physics - Theory

7 pages (plus one figure avaliable via direct request), LaTeX, Preprint IFUNAM FT 94-43

Scientific paper

10.1103/PhysRevA.50.5335

It is shown that the Coulomb correlation problem for a system of two electrons (two charged particles) in an external oscillator potential possesses a hidden $sl_2$-algebraic structure being one of recently-discovered quasi-exactly-solvable problems. The origin of existing exact solutions to this problem, recently discovered by several authors, is explained. A degeneracy of energies in electron-electron and electron-positron correlation problems is found. It manifests the first appearence of hidden $sl_2$-algebraic structure in atomic physics.

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