Weyl asymptotics for magnetic Schrödinger operators and de Gennes' boundary condition

Details Weyl asymptotics for magnetic Schrödinger operators and de Gennes' boundary condition Weyl asymptotics for magnetic Schrödinger operators and de Gennes' boundary condition

2007-09-07

arxiv.org/abs/0709.1032v4

Mathematics

Spectral Theory

28 pages (revised version). to appear in Rev Math Phys

Scientific paper

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)].

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