Results on the Aharonov-Bohm effect without contact with the solenoid
arXiv:1711.06525 · doi:10.1063/1.4992123
Abstract
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.
It is a report of results. Proofs appear elsewhere