  In this note, we first obtain the decomposition of the non-relativistic field
velocity into the classical part (i.e., the velocity w=p/m OF the
center-of-mass (CM), and the so-called quantum part (i.e., the velocity V of
the motion IN the CM frame (namely, the internal spin-motion or
Zitterbewegung), these two parts being orthogonal. Our starting point is the
Pauli current. Then, by inserting such a composite expression of the velocity
into the kinetic energy term of the non-relativistic newtonian lagrangian, we
get the appearance of the so-called "quantum potential" (which makes the
difference between classical and quantum behaviour) as a pure consequence of
the internal motion. Such a result carries further evidence about the
possibility that the quantum behaviour of micro-systems be a direct consequence
of the fundamental existence of spin.
