2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149210We construct exact wavefunctions of two vortices on a plane, a single vortex on the cylinder and a vortex on the torus. In each case, the physics is shown to be equivalent to a particle moving in a covering space, something simple to solve in those examples. We describe how our solutions fit into the general theory of quantum mechanics of $N$ particles on a two-dimensional space and attribute our success to the fact that the fundamental groups are Abelian in those simple cases that we are considering.Reference addedHigh Energy Physics - Theorytext