Two electrons in an external oscillator potential: Particular analytic solutions of a Coulomb correlation problem

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Abstract
The problem of the Schrödinger equation for two electrons (interacting with Coulomb potentials) in an external harmonic-oscillator potential is revisited and shown to be solvable analytically for a particular, denumerably infinite set of oscillator frequencies. Solutions are given for ground and excited states in the singlet and triplet spin configurations.