The spectra of two electrons in a parabolic quantum dot in a magnetic field are obtained using the WKB approximation. No restrictions are imposed on the value of the electron-electron interaction. A simple approximation allowing an exact solution to be obtained for the interaction between two electrons in a quantum dot is proposed. It reproduces all of the qualitative features of the two-electron spectrum. Quantitatively, it is in good agreement with the WKB solution for the range of parameters of experimental interest.
The dynamics of two-dimensional electrons in a circular ring in an external perpendicular magnetic field is investigated. The boundaries of the ring are approximated by infinite potential barriers. Within the quasiclassical approximation, a complete classification of the electron states generated by confinement and magnetic field is provided.
We derive the analytical form of the Green's function of 2-dimensional electrons with lateral confinement in a perpendicular magnetic field. The confinement potentials considered are infinite barriers at radius R (quantum dot) and at r a n d R (quantum ring).
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