  We study the localization of particles rotating in a two-dimensional harmonic
potential by solving their rotational spectrum using many-particle quantum
mechanics and comparing the result to that obtained with quantizing the rigid
rotation and vibrational modes of localized particles. We show that for a small
number of particles the localization is similar for bosons and fermions.
Moreover, independent of the range of the interaction the quantum mechanical
spectrum at large angular momenta can be understood by vibrational modes of
localized particles.
