On the spin-1/2 Aharonov-Bohm problem for modified Pöschl-Teller potential, physical regularization and self-adjoint extensions

Abstract

We study the bound-state energies for a spin-1/2 particle subjected to the modified Poschl-Teller potential and an Aharonov-Bohm field in the nonrelativistic limit. The problem of the $ \delta$ -function singularity which describes the interaction between spin and magnetic flux is solved using two different approaches already known in the literature, the first is a physical regularization based on a redefinition of the Aharonov-Bohm field as a limit of another one which is more physical and less singular. The second is the self-adjoint extensions method, we obtain an expression for the self-adjoint extension parameter in terms of the physics of the problem.