Abstract
We consider the Hamiltonian operator associated with planar sections of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space , we characterize all generalized boundary conditions on the solenoid border 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 conditions, that is, Dirichlet, Neumann and Robin.
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