Schr\"{o}dinger operators with multiple Aharonov-Bohm fluxes

We study the Schr\"{o}dinger operator describing a two-dimensional quantum particle moving in presence of $N \geqslant 1$ Aharonov-Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.