Mathematical justification of the Aharonov-Bohm hamiltonian

Details Mathematical justification of the Aharonov-Bohm hamiltonian Mathematical justification of the Aharonov-Bohm hamiltonian

2008-10-03

arxiv.org/abs/0810.0684v1

Physics

Mathematical Physics

to be published in Journal of Statistical Physics

Scientific paper

10.1007/s10955-008-9631-y

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.

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