  A quantum particle interacting with a thin solenoid and a magnetic flux is
described by a five-parameter family of Hamilton operators, obtained via the
method of self-adjoint extensions. One of the parameters, the value of the
flux, corresponds to the Aharonov-Bohm effect; the other four parameters
correspond to the strength of a singular potential barrier. The spectrum and
eigenstates are computed and the scattering problem is solved.
