2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170664It is presented, in the framework of nonrelativistic quantum mechanics, a justification of the usual Aharonov-Bohm hamiltonian (with solenoid of radius greater than zero). This is obtained by way of increasing sequences of finitely long solenoids together with a natural impermeability procedure; further, both limits commute. Such rigorous limits are in the strong resolvent sense and in both $\R^2$ and $\R^3$ spaces.to be published in Journal of Statistical PhysicsMathematical PhysicsSpectral Theorytext