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arXiv · 1008.2906

Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian

Cesar R. de Oliveira·Marciano Pereira
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Abstract

We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space $\mathcal H^2$, we characterize all generalized boundary conditions on the solenoid bor- der compatible with quantum mechanics, i.e., the boundary conditions so that the corresponding hamiltonian operators are self-adjoint. Then we study and compare the scattering of the most usual boundary con- ditions, that is, Dirichlet, Neumann and Robin.

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Cesar R. de Oliveira, Marciano Pereira. 2010-08-17. Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian. https://doi.org/10.1088/1751-8113/43/35/354011

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