  We consider a charged quantum particle immersed in an axial magnetic field,
comprising a local Aharonov-Bohm singularity and a regular perturbation.
Quadratic form techniques are used to characterize different self-adjoint
realizations of the reduced two-dimensional Schr\"odinger operator, including
the Friedrichs Hamiltonian and a family of singular perturbations indexed by $2
\times 2$ Hermitian matrices. The limit of the Friedrichs Hamiltonian when the
Aharonov-Bohm flux parameter goes to zero is discussed in terms of $\Gamma$ -
convergence.
