Classical bounds on quantum partition functions

Explicit bounds on the quantum partition functions are given in terms of classical partition functions, incorporating effective pair potentials, which account for Fermi- and Bose-statistics, respectively. The bounds may be used for the limit 0 and eventually for showing the interchangeability of the classical with the thermodynamic limit. A simple derivation of the thermodynamic limit for free particles with general dispersions is given.Work supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. 3569.