  We show that the well known geometric phase, the Gouy phase in optics can be
defined for matter waves in vacuum as well. In particular we show that the
underlying physics for the "matter waves" Gouy phase is the generalized
Schroedinger-Robertson uncertainty principle, more specifically, the off
diagonal elements of the covariance matrix. Recent experiments involving the
diffraction of fullerene molecules and the uncertainty principle are shown to
be quantitatively consistent with the existence of a Gouy phase for matter
waves.
