Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds

T. Mine

Abstract


We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in terms of the boundary conditions. The result is an extension of the former results by Dabrowski-Šťoviček and Exner-Šťoviček-Vytřas.

Keywords


Spectral theory; functional analysis; self-adjointness; Aharonov-Bohm effect; quantum mechanics; differential geometry; Schrödinger operator

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague