Quantum Corrections to the Equation of State for Nonanalytic Potentials

A method used by Hemmer and Jancovici to calculate quantum corrections to the equation of state for a hard-sphere gas is extended to cover the case of a more general intermolecular potential. The basis of the method is an expansion of the partition function about its classical limit, the terms in the expansion being integrals over products of classical correlation functions and certain "modified" quantum Ursell functions. Conditions are discussed under which this series can be truncated to give the quantum corrections to a specified order in $h$ (Planck's constant). A calculation of the first quantum correction is carried out for the square-well-plus-hard-core potential.