Solution of Percus’s equation for the density of hard rods in an external field

Abstract
The theory of a one-dimensional fluid of hard rods has received much attention because it often yields exact results which serve as a guide to understanding the properties of more complicated fluids. Of particular interest recently has been the density distribution of nonuniform fluids in external potentials or between solid walls. The purpose of this paper is to report an explicit solution of the nonlinear integral equation derived by Percus for the density distribution of hard rods.