  The solution of differential problems, and in particular of quantum wave
equations, can in general be performed both in the direct and in the reciprocal
space. However, to achieve the same accuracy, direct-space finite-difference
approaches usually involve handling larger algebraic problems with respect to
the approaches based on the Fourier transform in reciprocal space. This is the
result of the errors that direct-space discretization formulas introduce into
the treatment of derivatives. Here, we propose an approach, relying on a set of
sinc-based functions, that allows us to achieve an exact representation of the
derivatives in the direct space and that is equivalent to the solution in the
reciprocal space. We apply this method to the numerical solution of the Dirac
equation in an armchair graphene nanoribbon with a potential varying only in
the transverse direction.
