Quantum Statistical Mechanics in Classical Phase Space. V. Quantum Local, Average Global

One-particle energy eigenfunctions are used to obtain quantum averages in many particle systems. These are based on the effective local field due to fixed neighbors in classical phase space, while the averages account for the non-commutativity of the position and momentum operators. Used in Monte Carlo simulations for a one-dimensional Lennard-Jones fluid, the results prove more reliable than a high temperature expansion and a harmonic local field approach, and at intermediate temperatures agree with benchmark numerical results. Results are presented for distinguishable particles, fermions, and bosons.