- 03-267 Abderemane Morame, Fran oise Truc.
- Remarks on the spectrum of the Neumann problem with magnetic field in
the half space
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