Using the theory of self-adjoint extensions, we construct all the possible Hamiltonians describing the nonrelativistic Aharonov-Bohm effect. In general, the resulting Hamiltonians are not rotationally invariant so that the angular momentum is not a constant of motion. Using an explicit formula for the resolvent, we describe the spectrum and compute the generalized eigenfunctions and the scattering amplitude
Adami, R., Teta, A. (1998). On the Aharonov-Bohm Hamiltonian. LETTERS IN MATHEMATICAL PHYSICS, 43(1), 43-53 [10.1023/A:1007330512611].
On the Aharonov-Bohm Hamiltonian
Adami, R;
1998
Abstract
Using the theory of self-adjoint extensions, we construct all the possible Hamiltonians describing the nonrelativistic Aharonov-Bohm effect. In general, the resulting Hamiltonians are not rotationally invariant so that the angular momentum is not a constant of motion. Using an explicit formula for the resolvent, we describe the spectrum and compute the generalized eigenfunctions and the scattering amplitude
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