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arXiv · hep-th/9406018

Two electrons in an external oscillator potential: hidden algebraic structure

Alexander Turbiner
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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 $sl_2$-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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Alexander Turbiner. 1994-06-03. Two electrons in an external oscillator potential: hidden algebraic structure. https://doi.org/10.1103/physreva.50.5335

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