The method is based on the analysis of time evolution of electron states in the real lattice space. The Chebyshev polynomials of the first kind are used to approximate the time evolution operator. We demonstrate that the developed method is powerful and efficient since the computational scaling law is linear. We invoked the method to study the electronic properties of special twisted bilayer graphene whose atomic structure is quasi-crystalline. | Real space approach for the electronic calculation of twisted bilayer graphene using the orthogonal polynomial technique