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Article Dans Une Revue Journal of Mathematical Physics Année : 2005

REMARKS ON THE SPECTRUM OF THE NEUMANN PROBLEM WITH MAGNETIC FIELD IN THE HALF SPACE

Francoise Truc
Abderemane Morame
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Résumé

We consider a Schrodinger 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 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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Dates et versions

hal-00381535 , version 1 (05-05-2009)

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  • HAL Id : hal-00381535 , version 1

Citer

Francoise Truc, Abderemane Morame. REMARKS ON THE SPECTRUM OF THE NEUMANN PROBLEM WITH MAGNETIC FIELD IN THE HALF SPACE. Journal of Mathematical Physics, 2005, 46 (1), pp.1-13. ⟨hal-00381535⟩
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