As in the free particle case, the time dependent wave packet solution to the TDSE is the general superposition of pure energy states with the appropriate time-dependent phase factors,
where the factor 
is just for
normalization so that, as we show in the next paragraph, 
is
normalized so long as is 
. Also, we again regard
as sharply peaked near some value of incoming momentum,
.
There are three terms in this expression, associated with either the source, the reflected or the transmitted packet. Each is an integral of the form we analyzed in free space in Section 2. Explicitly, the three terms are
The complete scattering solution may be reassembled from these integrals,
