Wednesday, July 4, 2012

1207.0214 (F. M. Andrade et al.)

Self-adjoint extension approach for spin-1/2 Aharonov-Bohm systems in
conical space

F. M. Andrade, E. O. Silva, M. Pereira
Using two different approaches known in the literature, both based on self-adjoint extension method, we propose a general approach, which is based on the conditions imposed by the physical problem. One of the advantages is that this approach yields the self-adjoint extension parameter in terms of physics of the problem. We apply it for the spin-1/2 Aharonov-Bohm problem in conical space in the nonrelativistic limit. The self-adjoint extension parameter to the bound state and scattering scenarios are determined. Our proposal solves the problem of the arbitrariness of the self-adjoint extension parameter, proposed in Ref. [Phys. Rev. D \textbf{40}, 1346 (1989)]. The present method is general and suitable for addressing any quantum system with a singular Hamiltonian that possesses bound and scattering states. As an application, we apply it for the spin-1/2 Aharonov-Bohm problem plus a two-dimensional isotropic harmonic oscillator.
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