A confined noninteracting many electron system: Accurate corrections to a statistical model

We derive a correction term to the Fermi–Dirac energy for the system of Nel noninteracting electrons confined to a cube with sides of infinite potential. This correction term is compared to one derived by Pauncz [R. Pauncz, Acta Physica Academiae Scientarium Hungaricae 1 (1952) 277]. Both models are compared to the exact quantum mechanical result with systems of 1 to 5000 electrons being considered. Agreement is seen to increase with particle number.