  We propose a simple situation in which the magnetic Aharonov-Bohm potential
influences the values of the deficiency indices of the initial Schr\"odinger
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.
