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arXiv · 0709.1032

Weyl asymptotics for magnetic Schr\"odinger operators and de Gennes' boundary condition

Ayman Kachmar
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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)].

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Ayman Kachmar. 2007-09-07. Weyl asymptotics for magnetic Schr\"odinger operators and de Gennes' boundary condition. https://doi.org/10.1142/s0129055x08003468

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