A Family of Schrödinger Operators Whose Spectrum is an Interval

By approximation, I show that the spectrum of the Schr\"odinger operator with potential $V(n) = f(n\rho \pmod 1)$ for f continuous and $\rho > 0$, $\rho \notin \N$ is an interval.
Comment: Comm. Math. Phys. (to appear)