Statistical mechanics and path integrals for a finite number of bosons

Recent investigations show that the statistical mechanics of a finite numbe r of particles in ideal harmonic systems predict different results for the same physical properties, depending on the ensemble under consideration. Pa th integral methods for a finite number of bosons with equidistant energy l evels give the same answers for the mean energy, the specific heat and the condensation temperature, etc., irrespective of whether their calculation r esults from the density of states, from the partition function or from the generating function. We show that this contradiction is caused by the use o f approximate relations between quantum statistical expressions. (C) 1999 E lsevier Science Ltd. All rights reserved.