  The objective of this series of three papers is to axiomatically derive
quantum mechanics from classical mechanics and two other basic axioms. In this
first paper, Schreodinger's equation for the density matrix is fist obtained
and from it Schroedinger's equation for the wave functions is derived. The
momentum and position operators acting upon the density matrix are defined and
it is then demonstrated that they commute. Pauli's equation for the density
matrix is also obtained. A statistical potential formally identical to the
quantum potential of Bohm's hidden variable theory is introduced, and this
quantum potential is reinterpreted through the formalism here proposed. It is
shown that, for dispersion free {\it ensembles% }, Schroedinger's equation for
the density matrix is equivalent to Newton's equations. A general non-ambiguous
procedure for the construction of operators which act upon the density matrix
is presented. It is also shown how these operators can be reduced to those
which act upon the wave functions.
