Absence of Eigenvalues for the Periodic Schr\"odinger Operator with Singular Potential in a Rectangular Cylinder

I. Kachkovskii

Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 2, pp. 27-37.

Résumé

We consider the periodic Schrödinger operator on a $d$-dimensional cylinder with rectangular section. The electric potential may contain a singular component of the form $\sigma(x,y)\delta_{\Sigma}(x,y)$, where $\Sigma$ is a periodic system of hypersurfaces. We establish that there are no eigenvalues in the spectrum of this operator, provided that $\Sigma$ is sufficiently smooth and $\sigma\in L_{p,\operatorname{loc}}(\Sigma)$, $p>d-1$.

Détail

Keywords: Schrödinger operator, periodic coefficients, absolutely continuous spectrum.

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