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Cesar R. de Oliveira, Marciano Pereira
Mathematical justiﬁcation of the Aharonov-Bohm hamiltonian
ABSTRACT. It is presented, in the framework of nonrelativistic quantum me-
chanics, a justiﬁcation of the usual Aharonov-Bohm hamiltonian (with
solenoid of radius greater than zero). This is obtained by way of in-
creasing sequences of ﬁnitely long solenoids together with a natural
impermeability procedure; further, both limits commute. Such rigor-
ous limits are in the strong resolvent sense and in both $R^2$ and $R^3$