  It 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.
