The physical interpretation of the right-incident solutions
(13), is that Region s contains two beams of particles,
one, emanating from the source, carrying 
particles per unit
time toward the right, and the other, carrying
reflected
particles per unit time toward the left. Region c is the scattering
region about which we need say little. Finally, Region t contains a
single beam of particles transmitted through the scattering region and
carrying 
particles per unit time toward the right.
Knowing the magnitude of the currents gives the answer to the first
question of scattering theory, the probability of a particle being
scattered in either direction, to the left or to the right. The
probability of reflection 
is just the ratio of the number of
particles reflected per unit time, 
, to the total number of
particles incident from the source per unit time, 
. Similarly,
the probability of transmission is the ratio of 
to . In
either case and thus we expect,
Note that our original derivation of the form of the probability
current 
deals with the
entire wave function 
at point x and makes no
distinction between different component parts of the wave function
traveling in different directions whose currents may be evaluated
separately. At present, the separation between the incoming and
reflected currents is a new physical idea which we have brought into
our formalism. We shall justify it fully in the next section
where we show that in a solution to the TDSE
made of an identifiable incoming wave packet one first finds a
distinct wave packet traveling toward the
collision region which is made up in such a way that the only
significant contribution to the back in Region s comes from the
incoming beam. Later, a partially reflected wave packet, to which
only the reflected beam part of the solution to the TISE contributes,
returns back toward the source. It is the fact that incoming and
reflected beam parts are active at different times in the scattering
of a wave packet which gives the ultimate justification for our
physical separation of the two currents which occupy the same region
of space. Below, we will see that (15) does not tell
the whole story, but is really only valid in the approximation of an
incoming wave packet which is nearly a pure state of momentum.
