  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.
