  An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in
large N Chern-Simons theory coupled to a fundamental scalar has recently been
conjectured. We find a scaling limit of the theory in which the pole in this
$S$-matrix is near threshold. We argue that the theory must be well described
by non-relativistic quantum mechanics in this limit, and determine the relevant
Schroedinger equation. We demonstrate that the $S$-matrix obtained from this
Schroedinger equation agrees perfectly with this scaling limit of the
relativistic $S$-matrix; in particular the pole structures match exactly. We
view this matching as a nontrivial consistency check of the conjectured field
theory $S$-matrix.
