  In our previous papers we were interested in making a reconstruction of
quantum mechanics according to classical mechanics. In this paper we suspend
this program for a while and turn our attention to a theme in the frontier of
quantum mechanics itself---that is, the formation of operators. We then
investigate all the subtleties involved in forming operators from their
classical counterparts. We show, using the formalism of quantum phase-space
distributions, that our formation method, which is equivalent to Weyl's rule,
gives the correct answer. Since this method implies that eigenstates are not
dispersion-free we argue for modifications in the orthodox view. Many
properties of the quantum phase-space distributions are also investigated and
discussed in the realm of our classical approach. We then strengthen the
conclusions of our previous papers that quantum mechanics is merely an
extremely good approximation of classical statistical mechanics performed upon
the configuration space.
