Mathematical justification of the Aharonov-Bohm hamiltonian

Cesar R. de Oliveira, Marciano Pereira

Published 2008-10-03Version 1

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.