(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.
Categories: quant-ph gr-qc hep-th physics.atom-ph