This article is cited in 4 papers

Absence of Eigenvalues for the Periodic Schrödinger Operator with Singular Potential in a Rectangular Cylinder

I. Kachkovskii

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: 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 $\sigma\in L_{p,\operatorname{loc}}(\Sigma)$, $p>d-1$.

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

UDC: 517.984.56

Received: 05.12.2012

DOI: 10.4213/faa3107

 English version: Functional Analysis and Its Applications, 2013, 47:2, 104–112

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