  The ground states of N-electron parabolic quantum dots in the presence of a
perpendicular magnetic field are investigated. Rigorous lower bounds to the
ground-state energies are obtained. It is shown that our lower bounds agree
well with the results of exact diagonalization. Analytic results for the lower
bounds to the ground-state energies of the quantum dots in a strong magnetic
field (known as electron molecule) agree very well with numerically calculated
lower bounds.
