 03189 J.L. Borg, J.V. Pule
 Pauli Approximations to the SelfAdjoint Extensions of the AharonovBohm Hamiltonian
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Apr 23, 03

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Abstract. It is well known that the formal AharonovBohm Hamiltonian operator,
describing the interaction of a charged particle with a magnetic
vortex, has a fourparameter family of selfadjoint extensions, which
reduces to a twoparameter family if one requires that the Hamiltonian
commutes with the angular momentum operator. The question we study
here is which of these selfadjoint extensions can considered as
limits of regularised AharonovBohm Hamiltonians, that is Pauli
Hamiltonians in which the magnetic field corresponds to a flux tube
of nonzero diameter. We show that not all the selfadjoint extensions
in this twoparameter family can be obtained by these approximations,
but only two oneparameter subfamilies. In these two cases we can
choose the gyromagnetic ratio in the approximating Pauli Hamiltonian
in such a way that we get convergence in the norm resolvent sense to
the corresponding selfadjoint extension.
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