  We analyze the so-called classical limit of the quantum-mechanical canonical
partition function. In order to do that, we define accurately the density
matrix for symmetrized and antisymmetrized wave functions only (Bose-Einstein
and Fermi-Dirac), and find an exact relation between them and the density
matrix for non symmetrized functions (Maxwell-Boltzmann). Our results differ
from the generally assumed in a numerical factor N!, for which we suggest a
physical interpretation. We derive as well the reverse (and also exact)
relation, to find the canonical partition function for non-symmetrized wave
functions in terms of the corresponding function for fermions and bosons.
