Quantum Statistical Mechanics Results for Argon, Neon, and Helium Using Classical Monte Carlo

Quantum corrections to the classical pressure are obtained for Lennard-Jones models of argon, neon, and helium using classical Metropolis algorithm computer simulations. The corrections for non-commutativity are obtained to fourth order in Planck’s constant. Compared to the classical virial pressure on all isotherms at liquid-like densities, the quantum correction is found to be $\mathcal{O}({10}^{-2})$ for argon, $\mathcal{O}({10}^0)$ for neon, and ${\cal O}(10^{3})$ for helium. The first order correction due to wave function symmetrization is also obtained, but this is relatively negligible.