We show that a one-dimensional tight-binding electron moving in a slowly varying potential, $V_n=\lambda cos\left(\alpha n^{\nu }\right)$, where $n$ is the site index and $0<\mathrm{}\nu <1\mathrm{}$, has a mobility edge in its spectrum provided that $2\lambda$ is smaller than the total unperturbed bandwidth of the system. We study the nature of the localized and extended eigenstates of this system as a function of $\lambda$ and $\nu$.

• Received 11 July 1988

DOI:https://doi.org/10.1103/PhysRevLett.61.2144