Mathematical justification of the Aharonov-Bohm hamiltonian

Abstract

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 ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$ spaces.

to be published in Journal of Statistical Physics