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

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 ${\mathrm{sl}}_2$-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 appearance of a hidden ${\mathrm{sl}}_2$-algebraic structure in atomic physics.