  We analyze the structure of the scattering matrix, $S(k)$, for the one
dimensional Morse potential. We show that, in addition to a finite number of
bound state poles and an infinite number of anti-bound poles, there exist an
infinite number of redundant poles, on the positive imaginary axis, which do
not correspond to either of the other types. This can be solved analytically
and exactly. In addition, we obtain wave functions for all these poles and
ladder operators connecting them. Wave functions for redundant state poles are
connected via two different series. We also study some exceptional cases.
