Norm Convergence of Self-Adjoint Extensions of the Aharonov–Bohm Hamiltonian as Solenoid Length Goes to Infinity

摘要

With respect to the Aharonov-Bohm effect, we consider only solenoids of zero radius and their action on its plane of symmetry. We find all self-adjoint extensions in case of finite length solenoids and compare them with the case of infinitely long one. It is then shown a convergence in the uniform resolvent sense for each angular momentum sector of such self-adjoint extensions as the solenoid length goes to infinity.