For this example I have chosen initial conditions:

**y:***y*_{0}=0,*k*_{y0}=6, =5**z:***z*_{0}=20,*k*_{z0}=12, =5

(Compared to previous examples, I have just expanded the *y*
to match the *z* .)
The full wavefunction is just the product of these two factors:

*(y,z,t)* = *Y(y,t) Z(z,t)*

and the probability density is ^{*}.

Here are some pictures of the lump of probability as it begins its motion:

Here is a "multiple-time" image showing the probability
density at *t*=0,3,6,9,12,15,18,21,24:

Notice the expansion of the wave-packet with time and the classical looking trajectory.

If __one__ electron were fired with this wavefunction
it would hit the "ground" at exactly one spot. If we
fired electron after electron we would gradually build up the
probable range of hit locations given by this wavefunction.
Notice that much the same statement could be made of
cannons whose projectiles follow Newton's laws. However
we would attribute the variation in hit-location to
variation in the initial velocity (say, due to variation in
the amount of propellant or uncertainty in the angle of
elevation) or variation in the forces active (say, due
to varying wind conditions or atmospheric pressure).
In QM we state that there is irreducible uncertainty
even if the initial conditions and forces are identical
in each shot. Thus there is not really a trajectory at all.
The electron may be found here one time and there the following
shot. All we have is a moving blob of probability density
whose center may follow a path quite similar to the
exacting trajectory given by Newton's laws. Finally I'd like
to note that the above calculations, summing 150 Airy functions
to find the probability density at a single point, are quite
time consuming. It would be foolish to use this
method of
calculation on human-scale projectiles where macroscopic
variations in conditions would swamp the irreducible uncertainty
due to QM. Newtonian mechanics is a simple and accurate
approximation of QM valid in most any human-scale problem.

The ballistic motion can be seen in greater detail by examining the following QuickTime movie (0.2 Mb) on a frame-by-frame basis.