Abstract
Recent investigations show that the statistical mechanics of a finite number of particles in ideal harmonic systems predict different results for the same physical properties, depending on the ensemble under consideration. Path integral methods for a finite number of bosons with equidistant energy levels give the same answers for the mean energy, the specific heat and the condensation temperature, etc., irrespective of whether their calculation results from the density of states, from the partition function or from the generating function. We show that this contradiction is caused by the use of approximate relations between quantum statistical expressions.
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