  Starting from the Pauli current we obtain the decomposition of the
non-relativistic local velocity in two parts: one parallel and the other
orthogonal to the momentum. The former is recognized to be the ``classical''
part, that is the velocity of the center-of-mass, and the latter the
``quantum'' one, that is the velocity of the motion in the center-of-mass frame
(namely, the internal ``spin motion'' or {\em Zitterbewegung}). Inserting the
complete expression of the velocity into the kinetic energy term of the
classical non-relativistic (i.e., Newtonian) Lagrangian, we straightforwardly
derive the so-called ``quantum potential'' associated to the Madelung fluid. In
such a way, the quantum mechanical behaviour of particles appears to be
strictly correlated to the existence of spin and Zitterbewegung.
