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

Francoise Truc (1) , Abderemane Morame

1 IF - Institut Fourier

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.

Keywords: Neumann problem; magnetic field; spectral theory; eigenvalues.; eigenvalues

Domains: Mathematical Physics [math-ph]; Mathematical Physics [math-ph]

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⟩