On the Pauli operator for the Aharonov-Bohm effect with two solenoids

Details On the Pauli operator for the Aharonov-Bohm effect with two solenoids On the Pauli operator for the Aharonov-Bohm effect with two solenoids

2003-10-16

arxiv.org/abs/math-ph/0310029v1

Physics

Mathematical Physics

LaTeX source file with 3 figures, to appear in JMP

Scientific paper

We consider a spin-1/2 charged particle in the plane under the influence of two idealized Aharonov-Bohm fluxes. We show that the Pauli operator as a differential operator is defined by appropriate boundary conditions at the two vortices. Further we explicitly construct a basis in the deficiency subspaces of the symmetric operator obtained by restricting the domain to functions with supports separated from the vortices. This construction makes it possible to apply the Krein's formula to the Pauli operator.

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