Generalized boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field

The most general admissible boundary conditions are derived for an idealized Aharonov-Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; the other two parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic field. The generalized boundary conditions may be regarded as a combination of the Aharonov-Bohm effect with a point interaction. Spectral properties of the derived Hamtonians are studied in detail. (C) 2002 American Institute of Physics.