  The weak equivalence principle of gravity is examined at the quantum level in
two ways. First, the position detection probabilities of particles described by
a non-Gaussian wave-packet projected upwards against gravity around the
classical turning point and also around the point of initial projection are
calculated. These probabilities exhibit mass-dependence at both these points,
thereby reflecting the quantum violation of the weak equivalence principle.
Secondly, the mean arrival time of freely falling particles is calculated using
the quantum probability current, which also turns out to be mass dependent.
Such a mass-dependence is shown to be enhanced by increasing the
non-Gaussianity parameter of the wave packet, thus signifying a stronger
violation of the weak equivalence principle through a greater departure from
Gaussianity of the initial wave packet. The mass-dependence of both the
position detection probabilities and the mean arrival time vanish in the limit
of large mass. Thus, compatibility between the weak equivalence principle and
quantum mechanics is recovered in the macroscopic limit of the latter. A
selection of Bohm trajectories is exhibited to illustrate these features in the
free fall case.
