  A generalization of symmetrized density matrices in combination with the
technique of generating functions allows to calculate the partition function of
identical particles in a parabolic confining well. Harmonic two-body
interactions (repulsive or attractive) are taken into account. Also the
influence of a homogeneous magnetic field, introducing anisotropy in the model,
is examined. Although the theory is developed for fermions and bosons, special
attention is payed to the thermodynamic properties of bosons and their
condensation.
