On the Darwin--Howie--Whelan Equations for the Scattering of Fast Electrons Described by the Schrödinger Equation

The Darwin-Howie-Whelan equations are commonly used to describe and simulate the scattering of fast electrons in transmission electron microscopy. They a system infinitely many envelope functions, derived from Schr\"odinger equation. However, for simulation images only finite set functions is used, leading ordinary differential thickness direction specimen. We study mathematical structure this provide error estimates evaluate accuracy special approximations, like two-beam systematic-row approximation.