Extending the Tight‐Binding Model by Discrete Fractional Fourier Transform

Abstract

An extension of the tight‐binding approximation model using the discrete fractional Fourier transform is proposed. The quantum state between localized and delocalized states is formulated, where the intermediate state is continuously parameterized. The mixed features of the localized molecular‐like state and delocalized wave‐like state are confirmed when the wavefunction and band diagram of the intermediate state are represented. The proposed model is expected to be used to represent the quantum state with localized/delocalized features in, for example, organic semiconductors.