Efeito Aharonov-Bohm sem interação com a fronteira do solenóide

Abstract

One of the biggest problem in the mathematical modeling of the Aharonov- Bohm Effect is the interaction between the electron and the solenoid border. Such interaction translates into boundary conditions on that border, which causes great ambiguity because in principle it is not clear what the most appropriate choice. In quantum mechanics this conditions represent self-adjoint extensions of the Schrödinger operator of the problem. On the other hand, recent works has demostrated that it is possible to confine quantum particles in certain regions of Rn with magnetic fields sufficientily intense near the border of that region. Mathematically this corresponds to essentially selfadjoint Schrödinger operators, which means exemption from the particle interation with the solenoid border In this work we intend to combine the two situations mentions above to study the Aharonov-Bohm effect in the plane, adding then external magnetic fields and potentials that are suffiently intense in the solenoid border so that the related Schrödinger operator is essentially self-adjoint.