Weyl asymptotics for magnetic Schr\"odinger operators and de Gennes' boundary condition
Spectral Theory
2015-05-13 v4
Abstract
This paper is concerned with the discrete spectrum of the self-adjoint realization of the semi-classical Schr\"odinger operator with constant magnetic field and associated with the de Gennes (Fourier/Robin) boundary condition. We derive an asymptotic expansion of the number of eigenvalues below the essential spectrum (Weyl-type asymptotics). The methods of proof relies on results concerning the asymptotic behavior of the first eigenvalue obtained in a previous work [A. Kachmar, J. Math. Phys. Vol. 47 (7) 072106 (2006)].
Keywords
Cite
@article{arxiv.0709.1032,
title = {Weyl asymptotics for magnetic Schr\"odinger operators and de Gennes' boundary condition},
author = {Ayman Kachmar},
journal= {arXiv preprint arXiv:0709.1032},
year = {2015}
}
Comments
28 pages (revised version). to appear in Rev Math Phys