The Friedrichs extension of the Aharonov-Bohm Hamiltonian on a disk. Integral Equations and Operator Theory

Abstract. We show that the Aharonov-Bohm Hamiltonian considered on a disc has a four-parameter family of self-adjoint extensions. Among the infinitely many self-adjoint extensions, we determine to which parameters the Friedrichs extension H F corresponds and its lowest eigenvalue is found. Moreover, we note that the diamagnetic inequality holds for H F. 1