  We present a nonrelativistic one-particle quantum mechanics whose
perturbative S-matrix exhibits a renormalon divergence that we explicitely
compute. The potential of our model is the sum of the 2d Dirac
$\delta$-potential -- known to require renormalization -- and a 1d Dirac
$\delta$-potential tilted at an angle. We argue that renormalons are not
specific to this example and exist for a much wider class of potentials. The
ambiguity in the Borel summation of the perturbative series due to the
renormalon pole is resolved by the physical condition of causality through
careful consideration of the $i\epsilon$ prescription. The suitably summed
perturbative result coincides with the exact answer obtained through the
operator formalism for scattering.
