The problem of computing the properties of a low mass quantum particle in equilibrium in a disordered medium is considered. With the advancement of computational speed, statistical methods for sampling a complex phase space are now viable. The Feynman-Kac path integral establishes a connection between a quantum particle and classical polymer consisting of p atoms. This allows the computation of quantum mechanical equilibrium values using well known methods devised for classical systems. Here we review the application of the path integral to the computation the properties of thermalized positron and positronium and introduce some new directions of investigation.