Incommensurate stacked 2D materials have gained significant attention after the recent discovery of a new mechanism of superconductivity in systems with small twist angles. Theoretically, the electronics of such systems are studied through tight-binding models. These models can be studied in several different spaces, though momentum space is often the leading favorite for physicists because this space often exhibits quasi-band structure. Deriving momentum space models is not a simple task, and typically has to be done starting from real space models.

In this work, we generalize the transformations found in incommensurate 2D systems between real space, configuration space, momentum space, and reciprocal space to study electronic observables and quasi-band structure of incommensurate bilayers using a wide class of applicable incommensurate Hamiltonians. We then apply this generalization to obtain the highly relevant effects of mechanical relaxation on nearly aligned materials in momentum space, which produce in-plane incommensurate scattering as well as longer ranged interlayer couplings. The long range coupling likewise changes the momentum space numerical scheme convergence rate. We study this convergence theoretically, and perform a numerical study on twisted bilayer graphene at small angles with mechanical relaxation using physically accurate tight binding models.