03-267 Abderemane Morame, Fran oise Truc.

Remarks on the spectrum of the Neumann problem with magnetic field in the half space (385K, postcript) Jun 6, 03

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Abstract. We consider a Schr dinger operator with a constant magnetic field in a half 3-dimensional space, with Neumann-type boundary conditions. It is known from the works by Lu-Pan and Helffer-Morame that the lower bound of its spectrum is less than the intensity b of the magnetic field, provided that the magnetic field is not normal to the boundary. We prove that the spectrum under b is a finite set of eigenvalues (each one of infinite multiplicity) . In the case when the angle between the magnetic field and the boundary is small, we give a sharp asymptotic expansion of the number of these eigenvalues.

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