%0 Journal Article
%T Two electrons in an external oscillator potential: hidden algebraic structure
%A Alexander Turbiner
%J Physics
%D 1994
%I arXiv
%R 10.1103/PhysRevA.50.5335
%X 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.
%U http://arxiv.org/abs/hep-th/9406018v1