In previous notes, we argued that the Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distributions are derivable from elastic scattering balance arguments. For example, for FD or BE cases, one may use e1+e2=e3+e4 and f(e1)[1 -/+ f(e3)] f(e2) [1 -/+ f(e4)] = f(e3)[1 -/+ f(e1)] f(e4)[1 -/+ f(e2)] ((1a)). Taking ln of the latter and linking to the former yields the distributions. For the BE case, there is an enhancement (1) of f(ei)+1 for a boson to scatter into a state ei occupied by f(ei) bosons. This follows from assuming that n bosons (a,b,c, etc) scatter into states (1,2,3…) with such similar momenta (magnitude and direction) that they may be treated as the same state. Thus, there is a lack of resolution in momentum phase space and also overcounting. In this note, we try to consider the interplay between quantum statistical behaviour of exp(ipx) waves and the statistical approach of scattering. Scattering assumes a specific energy and momentum, but single particle wavefunctions, especially those inside a “box” have a momentum distribution with an average momentum and distributions (e.g. sin(px)). As a result, the single particle wavefunction only represents the average momentum for a portion of the time (hopefully a large portion). Nevertheless, we ask whether one may obtain a more accurate result by considering a factor A(ei) related to the variance of the momentum wavefunction and replacing f(ei) with W(ei)f(ei). In a collision, both momentum and energy come into play. Thus, different wavefunctions (due to different potentials) have different momentum distributions which seem to affect the scattering picture used in (1), in particular the resolution of the scattered states. For example, nucleons in a hot nucleus may be approximated as almost being in a “box” (i.e. a Fermi gas). In this note, we find that the overall form of the FD or BE distribution may remain the same, but are multiplied by a factor 1/A(ei) which seems to play the role of modifying the phase space cell size.