On the asymptotic number of edge states for magnetic Schrödinger operators
Rupert L. Frank
Abstract
We consider a Schrödinger operator (h D - A)2 with a positive magnetic field B= A in a domain Ω⊂2. The imposing of Neumann boundary conditions leads to spectrum below h∈f B. This is a boundary effect and it is related to the existence of edge states of the system. We show that the number of these eigenvalues, in the semi-classical limit h 0, is governed by a Weyl-type law and that it involves a symbol on ∂Ω. In the particular case of a constant magnetic field, the curvature plays a major role.
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