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The quantum mechanical many-body problem is rarely analytically solvable. Onenotable exception is the case of two electrons interacting via a Coulombpotential in a uniform magnetic field. The motion is confined to atwo-dimensional plane, which is commonly the case in nanodevices. We comparethe exact solution with the semiclassical energy spectrum and study thetime-dependent dynamics of the system using the time-dependent variationalprinciple.

Two interacting electrons in a magnetic field: comparison of semiclassical, quantum, and variational solutions