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

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.

40 pages, 5 figures

References in corpus (2)

• Aharonov-Bohm Effect with $\delta$--type Interaction
• Mathematical justification of the Aharonov-Bohm hamiltonian

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