Particular analytical solutions of the two-dimensional Schrodinger equation are described for two electrons (interacting with Coulomb potentials) in a homogeneous magnetic field B and an external oscillator potential with frequency omega 0 . These exact solutions occur at an infinite and countable set of values of the quantity omega = square root ( omega 0 2 + 1/4 (B/c) 2 ). Additionally, approximate closed-form solutions for the limits of small omega (perturbation theory in the electron-electron interaction) and large omega (harmonic approximation) are discussed and compared with the exact solutions.
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M. Taut (1994) studied this question.
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