Quantum Corrections to the Second Virial Coefficient at High Temperatures

The Laplace transform of exp (−βH) is the Green's operator of the negative-energy Schrödinger equation (H + W)−1. Conditions are stated under which a large |W| asymptotic series for the Green's operator can be inverse-Laplace-transformed term-by-term to obtain a small β expansion for exp (−βH). This approach and the Watson transformation are used to calculate the first few terms of high-temperature asymptotic expansions for the exchange second virial coefficient for hard spheres and for the Lennard-Jones potential. The known results for the direct second virial coefficient for hard spheres are extended. The Wigner-Kirkwood expansion is calculated to order ℏ6 and used to calculate the direct second virial coefficient for the Lennard-Jones potential through order ℏ6.

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