  We discussed exact solutions of the Schroedinger equation for a
two-dimensional parabolic confinement potential in a homogeneous external
magnetic field. It turns out that the two-electron system is exactly solvable
in the sense, that the problem can be reduced to numerically solving one radial
Schroedinger equation. For a denumerably infinite set of values of the
effective oscillator frequency
$\tilde{\omega}=\sqrt{\omega_0^2+(\omega_c/2)^2}$ (where $\omega_0$ is the
frequency of the harmonic confinement potential and $\omega_c$ is the cyclotron
frequency of the magnetic field) even analytical solutions can be given.
  Our solutions for three electrons are exact in the strong - and the weak
correlation limit. For quantum dot lattices with Coulomb-correlations between
the electrons in different dots exact solutions are given, provided the lattice
constant is large compared with the dot diameters. We are investigating basic
physical properties of these solutions like the formation and distortion of
Wigner 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 system
for the semi-relativistic Current-Density-Functional Theory.
