Semiclassical corrections to the interaction energy of a hard-sphere Boltzmann gas

Details Semiclassical corrections to the interaction energy of a hard-sphere Boltzmann gas Semiclassical corrections to the interaction energy of a hard-sphere Boltzmann gas

2006-07-13

arxiv.org/abs/cond-mat/0607331v1

Eur. J. Phys. 27 (2006) 1323-1329

Physics

Condensed Matter

Statistical Mechanics

9 pages, 3 figures, submitted to Eur. J. Phys

Scientific paper

10.1088/0143-0807/27/6/006

Quantum effects in statistical mechanics are important when the thermal wavelength is of the order of, or greater than, the mean interatomic spacing. This is examined at depth taking the example of a hard-sphere Boltzmann gas. Using the virial expansion for the equation of state, it is shown that the interaction energy of a classical hard-sphere gas is exactly zero. When the (second) virial coefficient of such a gas is obtained quantum mechanically, however, the quantum contribution to the interaction energy is shown to be substantial. The importance of the semiclassical corrections to the interaction energy shows up dramatically in such a system.

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