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hal-00381535, version 1

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

Francoise Truc () 1, Abderemane Morame ()

Journal of Mathematical Physics 46, 1 (2005) 1-13

Abstract: 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.

  • 1:  Institut Fourier (IF)
  • CNRS : UMR5582 – Université Joseph Fourier - Grenoble I
  • Collaboration : Abderemane Morame
  • Domain : Mathematics/Mathematical Physics
    Physics/Mathematical Physics
  • Keywords : Neumann problem – magnetic field – spectral theory – eigenvalues.
  • Internal note : Institut Fourier
 
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  • From: Francoise Truc <>
  • Submitted on: Tuesday, 5 May 2009 16:52:58
  • Updated on: Tuesday, 5 May 2009 16:55:22