Numerical Estimation of the Partition Function in Quantum Statistics

A method for estimating the partition function of a quantum mechanical system is described. The method is based on a technique for evaluating the Wiener integrals in terms of which the partition function may be expressed. This technique involves first, an approximation of the Wiener integral by an n-dimensional integral and, second, a Monte Carlo estimation of the value of the n-dimensional integral. Application of the method to a harmonic oscillator and a pair of interacting particles in a box in two dimensions is described.