I will present some results on Schrödinger operators with a magnetic
potential of Aharonov-Bohm type. This means that the magnetic potential
has singularities at a finite number of points called poles. On a bounded
planar domain, we define the corresponding magnetic Hamiltonians with
Dirichlet boundary conditions, and study their eigenvalues as functions of
the poles. The nodal sets of the eigenfunctions is connected to a spectral
minimal partition problem. These eigenvalues are shown to be continuous. Using Kato-Rellich theory,
they can even be shown to be analytic under some restrictive conditions.