Exact Solution of Schrödinger Equation in Aharonov-Bohm plus Dirac-Monopole Potential

An exact solution of the Schrödinger equation for a charge $e$ in the potential of a flux tube along the $z$ axis and a Dirac magnetic monopole of strength $g$ at the origin is obtained. Single-valued solutions exist even with $2eg\ne \mathrm{integer}$. When $2eg=\mathrm{integer}$ and single-valuedness holds, solutions with $\left|J_z\mathrm{}\right|<\mathrm{}\left|eg\right|$ have a centrifugal barrier (and hence behavior at the origin) independent of flux, but solutions with $\left|J_z\mathrm{}\right|>\mathrm{}\left|eg\right|$ have a flux-dependent centrifugal barrier.