In this paper, we apply the effective potentials in the localization
landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the
spectral properties of the incommensurate systems. We uniquely develop a plane
wave method for the effective potentials of the incommensurate systems and
utilize that, the localization of the electron density can be inferred from the
effective potentials. Moreover, we show that the spectrum distribution can also
be obtained from the effective potential version of Weyl's law. We perform some
numerical experiments on some typical incommensurate systems, showing that the
effective potential provides an alternative tool for investigating the
localization and spectrum distribution of the systems.Comment: 14page