Canonical and microcanonical ensemble approaches to Bose-Einstein condensation: The thermodynamics of particles in harmonic traps

The thermodynamic properties of bosons moving in a harmonic trap in an arbi trary number of dimensions are investigated in the grand canonical, canonic al and microcanonical ensembles by applying combinatorial techniques develo ped earlier in statistical nuclear fragmentation models. Thermodynamic func tions such as the energy and specific heat are computed exactly in these en sembles. The occupation of the ground or condensed state is also obtained e xactly, and signals clearly the phase transition. The application of these techniques to fermionic systems is also briefly discussed.