- 03-189 J.L. Borg, J.V. Pule
- Pauli Approximations to the Self-Adjoint Extensions of the Aharonov-Bohm Hamiltonian
(272K, PDF)
Apr 23, 03
-
Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers
-
Abstract. It is well known that the formal Aharonov-Bohm Hamiltonian operator,
describing the interaction of a charged particle with a magnetic
vortex, has a four-parameter family of self-adjoint extensions, which
reduces to a two-parameter family if one requires that the Hamiltonian
commutes with the angular momentum operator. The question we study
here is which of these self-adjoint extensions can considered as
limits of regularised Aharonov-Bohm Hamiltonians, that is Pauli
Hamiltonians in which the magnetic field corresponds to a flux tube
of non-zero diameter. We show that not all the self-adjoint extensions
in this two-parameter family can be obtained by these approximations,
but only two one-parameter 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 self-adjoint extension.
- Files:
03-189.src(
03-189.keywords ,
AB.pdf.mm )