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We discussed exact solutions of the Schroedinger equation for atwo-dimensional parabolic confinement potential in a homogeneous externalmagnetic field. It turns out that the two-electron system is exactly solvablein the sense, that the problem can be reduced to numerically solving one radialSchroedinger equation. For a denumerably infinite set of values of theeffective oscillator frequency$\tilde{\omega}=\sqrt{\omega_0^2+(\omega_c/2)^2}$ (where $\omega_0$ is thefrequency of the harmonic confinement potential and $\omega_c$ is the cyclotronfrequency of the magnetic field) even analytical solutions can be given.  Our solutions for three electrons are exact in the strong - and the weakcorrelation limit. For quantum dot lattices with Coulomb-correlations betweenthe electrons in different dots exact solutions are given, provided the latticeconstant is large compared with the dot diameters. We are investigating basicphysical properties of these solutions like the formation and distortion ofWigner molecules, the dependence of the correlation strength from $\omega_0$and $\omega_c$, and we show that in general there is no exact Kohn- Sham systemfor the semi-relativistic Current-Density-Functional Theory.

Exact solutions for a two-electron quantum dot model in a magnetic field and application to more complex systems