Two electrons in an external oscillator potential: hidden algebraic structure

Abstract

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 $s{l}_2$-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 $s{l}_2$-algebraic structure in atomic physics.

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