Nature of the Quantum Corrections to the Statistical Model

Abstract

The scheme of correcting the Fermi-Thomas particle density formula by a power series in $\hslash$, procedures for which have been proposed by a number of authors, is examined through its application to a one-dimensional linear potential, which yields an analytical expression for the exact wave mechanical density for comparison. It is concluded that this is an asymptotic series, valid only where the particle density is large. Furthermore, terms of an oscillatory nature, which may very well transcend the so-called quantum corrections, are missing. A reason for this is offered.