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

Abstract

The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane, which is commonly the case in nanodevices. We compare the exact solution with the semiclassical energy spectrum and study the time-dependent dynamics of the system using the time-dependent variational principle.

13 pages, 3 figures

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Cited by in corpus (5)

• Exact treatment of planar two-electron quantum dots: effects of anharmonicity on the complexity
• Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator
• Time-dependent approach to transport and scattering in atomic and mesoscopic physics
• Interacting electrons in a magnetic field in a center-of-mass free basis
• Transient capture of electrons in magnetic fields, or: comets in the restricted three-body problem