  Recent investigations show that the statistical mechanics of a finite number
of particles in ideal harmonic systems predicts 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 whether their calculation results
from the density of states, from the partition function or from the generating
function.
  We show that this contradiction is due either to the use of approximate
relations between quantum statistical expressions, or to a misinterpretation of
the generating function.

Statistical Mechanics