Spinless Aharonov-Bohm problem in curved space

(Dated: February 26, 2015)The dynamics of a spinless charged particle under the influence of a magnetic field in curved spaceis considered. We chose the surface as being a cone defined by a line element in polar coordinates.The geometry of this line element establishes that the motion of the particle can occur on the surfaceof a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also becauseof two-dimensional confinement, the geometric potential should be taken into account. At first, weestablish the conditions for the particle describing a circular path in such a context. Because of thepresence of the geometric potential, which contains a singular term, we use the self-adjoint extensionmethod in order to describe the dynamics in all space including the singularity. Expressions areobtained for the bound state energies and wave functions.