Abstract
We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the -function singularity coming from the Zeeman spin interaction with the magnetic flux tube is solved through the self-adjoint extension method. Using two different approaches already known in the literature, both based on the self-adjoint extension method, we obtain the self-adjoint extension parameter to the bound state and scattering scenarios in terms of the physics of the problem. It is shown that such a parameter is the same for both situations. The method is general and is suitable for any quantum system with a singular Hamiltonian that has bound and scattering states.
- Received 4 December 2011
DOI:https://doi.org/10.1103/PhysRevD.85.041701
© 2012 American Physical Society