Absolute continuity of the periodic Schrodinger operator in transversal geometry
Open Access Publications from the University of California

## Absolute continuity of the periodic Schrodinger operator in transversal geometry

• Author(s): Krupchyk, K
• Uhlmann, G
• et al.

## Published Web Location

https://doi.org/10.4171/JEMS/673
Abstract

We show that the spectrum of a Schr\"odinger operator on $\mathbb{R}^n$, $n\ge 3$, with a periodic smooth Riemannian metric, whose conformal multiple has a product structure with one Euclidean direction, and with a periodic electric potential in $L^{n/2}_{\text{loc}}(\mathbb{R}^n)$, is purely absolutely continuous. Previously known results in the case of a general metric are obtained in [12], see also [8], under the assumption that the metric, as well as the potential, are reflection symmetric.

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