Pade approximant method for the statistical thermodynamics of a quantum system. I. General formulation and simple examples

Abstract

The method of two-point Pade approximants is used to interpolate between the low-temperature and high-temperature behaviour of the thermodynamic partition function of a quantum system. The system is assumed to have low-lying discrete energy levels which dominate the low-temperature behaviour. A method of successive approximation is introduced, which allows more information from both regions to be included at each step. Other thermodynamic quantities can be calculated either by an extension of the method, or by differentiating the approximations found for the partition functions. The method is applied to three simple systems (the harmonic oscillator, the rigid rotator, and the particle in a box) and shown to give good results for all temperatures.