Classical limit of the canonical partition function
Statistical Mechanics
2015-06-16 v1 Quantum Gases
Abstract
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.
Keywords
Cite
@article{arxiv.1307.7108,
title = {Classical limit of the canonical partition function},
author = {Pere Seglar and Enric Pérez},
journal= {arXiv preprint arXiv:1307.7108},
year = {2015}
}