  (abridged)If the space-time is presupposed, the coordinate representation of
the solutions $\psi(\vec x, t)$ of the Schroedinger equation of a quantum
system containing one massive scalar particle has a {\it preferred status}. It
is then possible to perform a multipolar expansion of the density matrix
$\rho(\vec x, t) = |\psi(\vec x, t)|^2$ (and more generally of the Wigner
function) around a space-time trajectory ${\vec x}_c(t)$ to be properly
selected. A special set of solutions $\psi_{EMWF}(\vec x, t)$, named {\it
Ehrenfest monopole wave functions}(EMWF), is characterized by the conditions
that: (i) the quantum expectation value of the position operator coincides at
any time with the searched classical trajectory, $< \psi_{EMWF} | {\hat {\vec
x}} | \psi_{EMWF}> = {\vec x}_c(t)$: this is possible only when the dipole
vanishes; (ii) Ehrenfest's theorem holds for the expectation values of the
position and momentum operator: its application to EMWF leads then to a {\it
closed Newton equation of motion for the classical trajectory, where the
effective force is the Newton force plus non-Newtonian terms (of order
$\hbar^2$ or higher) depending on the higher multipoles of the probability
distribution $\rho$.} These results can be extended to N particle systems and
to relativistic quantum mechanics. There is substantial agreement with Bohr's
viewpoint: the macroscopic description of the preparation, certain intermediate
steps and the detection of the final outcome of experiments involving massive
particles are dominated by these 'classical {\it effective} trajectories'. In
the framework of decoherence, one gets a transition from an {\it improper
quantum} mixture to a {\it classical statistical} one, when both the particle
and the pointer wave functions appearing in the reduced density matrix are
EMWF.
