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arXiv · 1112.0265

Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space

F. M. Andrade·E. O. Silva·M. Pereira
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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 δ-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.

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F. M. Andrade, E. O. Silva, M. Pereira. 2012-02-23. Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space. https://doi.org/10.1103/physrevd.85.041701

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