# Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder

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## 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 *σ*(*x, y*)*δ* _{Σ}(*x,y*), where Σ is a periodic system of hypersurfaces. We establish that there are no eigenvalues in the spectrum of this operator, provided that Σ is sufficiently smooth and *σ* ∈ *L* _{ p,loc}(Σ), *p* > *d* − 1.

## Key words

Schrödinger operator periodic coefficients absolutely continuous spectrum## Preview

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