arXiv subjects
Publications and source records attributed to Renan G. Romano.
We propose a simple situation in which the magnetic Aharonov-Bohm potential influences the values of the deficiency indices of the initial Schrödinger operator, so determining whether the particle interacts with the solenoid or not. Even with the particle excluded from the magnetic field, the number of self-adjoint extensions of the initial Hamiltonian depends on the magnetic flux. This is a new point of view of the Aharonov-Bohm effect.
We add a confining potential to the Aharonov-Bohm model resulting in no contact of the particle with the solenoid (border); this is characterized by a unique self-adjoint extension of the initial Hamiltonian operator. It is shown that the spectrum of such extension is discrete and the first eigenvalue is found to be a nonconstant 1-periodic function of the magnetic flux circulation with a minimum at integers and maximum at half-integer circulations. This is a rigorous verification of the effect.