Abstract
We studied scattering of quantum particles by geometry. Firstly, we re-visited an old subject to discuss relationships between the dynamics for particles subjected to potentials and the dynamics for particles moving freely on background geometries, in the context of non-relativistic quantum mechanics. We illustrated how selected geometries can be used to regularize singular potentials, and in this context, we computed scattering amplitudes for quanta incident on a static non-relativistic wormhole. Secondly, we studied selected spatial geometries that can either enhance or suppress scattering amplitudes, to produce either extremely sharp resonances and/or very strong cloaking for a specified angular momentum. We presented in detail a simple model for an impenetrable sphere surrounded by a Riemannian step geometry. Lastly, we considered the scattering of particles by a variety of geometrical holes and computed quantum scattering cross-sections for simple models where non-relativistic particles are incident on a selection of specified hole geometries in various spatial dimensions.