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An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering inlarge N Chern-Simons theory coupled to a fundamental scalar has recently beenconjectured. 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 describedby non-relativistic quantum mechanics in this limit, and determine the relevantSchroedinger equation. We demonstrate that the $S$-matrix obtained from thisSchroedinger equation agrees perfectly with this scaling limit of therelativistic $S$-matrix; in particular the pole structures match exactly. Weview this matching as a nontrivial consistency check of the conjectured fieldtheory $S$-matrix.

Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics