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

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

2010-08-17

arxiv.org/abs/1008.2906v1

J. Phys. A: Math. Theor. 43 (2010) 354011

Physics

Mathematical Physics

40 pages, 5 figures

Scientific paper

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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