Integral and Differential Equations of the Dynamical Theory of Electron Diffraction within a Distribution Formalism

Using the distributions theory, an integral formulation is developed of electron dynamical theory including boundaries conditions. Two methods are proposed and the results are given in the general case of forward and backward diffusion. A differential formalism is derived in the second, first, and zeroth order. I n the column approximation, the Howie‐Whelan's formulation may be regarded as the convolution inverse of the integral form. It is suggested that this formalism is very useful as a basis for perturbation methods, diffuse scattering, and image formation.