Article ID Journal Published Year Pages File Type
1856011 Annals of Physics 2015 13 Pages PDF
Abstract

•Motion of particle under the influence of magnetic field in curved space.•Bound state for Aharonov–Bohm problem.•Particle describing a circular path.•Determination of the self-adjoint extension parameter.

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov–Bohm potential in curved space is 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 surface of a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also because of two-dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in such a context. Because of the presence of the geometric potential, which contains a singular term, we use the self-adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions.

Related Topics
Physical Sciences and Engineering Physics and Astronomy Physics and Astronomy (General)
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