The spatial probability distributions 
associated
with the 
are uniform and constant. Yet, we associate
these states with particular values of momentum. It is the
probability current,
which shows the flow of particles associated with these states.
Evaluating the current for the gives
In the last line, we have used the fact that the probability density
of this state is 
and identified 
, the
velocity which we would classically expect to be associated with a
particle of mass m traveling with momentum 
.
The form (3) for j(x) gives a clear physical
interpretation for the . The represent constant beams of
particles of density 
traveling at velocity 
. It is
important to keep in mind that the simple result (3)
does not hold in general except for wave functions of the simple plane
wave form 
. Nonetheless, (3) is a good
mnemonic for remembering an expression which we will use time and time
again in scattering theory.
