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Energy of surface states for 3D magnetic Schrödinger operators

by Marwa Nasrallah
PhD Dissertations | November 2013
In this dissertation, we study the Schrödinger operator with magnetic field in a three dimensional domain with compact smooth boundary. Functions in the domain of the operator satisfy (magnetic) Neumann condition on the boundary. The operator depends on the semi-classical parameter. As this parameter becomes small, certain eigenfunctions of the operator are localized near the boundary of the domain, hence they will be called surface states. The main result of this dissertation is the calculation of the leading order terms of the energy and the number of surface states when the semi-classical parameter tends to zero.
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Thesis advisor: Søren Fournais, Aarhus University and Ayman Kachmar, Lebanese University