Electron localization in a quasiperiodic array of potential wells

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Abstract
We have solved the Schrödinger equation for a potential consisting of an array of barriers the widths of which are modulated incommensurately. The Lyapunov exponent as a function of eigenenergy has been calculated to determine the localization properties of eigenstates in the entire spectrum. When the strength of the potential modulation is increased, the transition of the eigenstate from extended to localized character is energy dependent, in contrast to the energy-independent transition appearing in the Aubry model. In certain limits, our results reduce to those obtained by other authors using simplified models.