Solution of quantum wave equations using cardinal sine functions

Abstract

We propose a method to solve differential problems, and in particular quantum wave equations, with periodic boundary conditions, in the direct space using periodic repetitions of the cardinal sine functions as basis functions, and we adopt it for the solution of the Schrödinger equation and, in graphene nanoribbons, of the Dirac equation. We show that this method, unlike finite-difference approaches, allows to avoid the errors deriving from the numerical approximation of the derivatives, and, if all of the terms of the equations are properly handled, is equivalent to a reciprocal space solution.