A family of Schrödinger operators whose spectrum is an interval

Abstract

By approximation, I show that the spectrum of the Schrödinger operator with potential $V(n)=f(n\rho (\mathrm{mod}1))$ for f continuous and $\rho >0$, $\rho \notin \mathbb{N}$ is an interval.

Comm. Math. Phys. (to appear)