On the role of spin in quantum mechanics

From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an "external" motion, which can be interpreted as the motion of the centre of mass, and an "internal" one, whose presence disappears in the classical limit. The latter is caused by the spin of the particle, whatever is its actual value (different from zero). The quantum potential in the Schrodinger equation, which is responsible of the quantum effects of the system, is then completely determined from the properties of the internal motion and its "unusual" properties have a simple and physical explanation in the present context. From the impossibility to fix the initial conditions relevant for the internal motion follows, finally, the need of a probabilistic interpretation of quantum mechanics.