An all orders formula for the S-matrix for 2 β 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.Comment: 12 pages, minor correction