  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.
