Friday, February 24, 2012

1112.0265 (F. M. Andrade et al.)

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

F. M. Andrade, E. O. Silva, M. Pereira
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 \delta-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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