  In this work we determine a lower bound to the mean value of the quantum
potential for an arbitrary state. Furthermore, we derive a generalized
uncertainty relation that is stronger than the Robertson-Schr\"odinger
inequality and hence also stronger than the Heisenberg uncertainty principle.
The mean value is then associated to the nonclassical part of the covariances
of the momenta operator. This imposes a minimum bound for the nonclassical
correlations of momenta and gives a physical characterization of the classical
and semiclassical limits of quantum systems. The results obtained primarily for
pure states are then generalized for density matrices describing mixed states.
