The scattering of high-energy electrons. I. Feynman path-integral formulation

The Feynman path-integral formulation of quantum mechanics is used to investigate the theoretical problem of the propagation of high-energy electrons through thin crystalline specimens. The primary objective is to find a satisfactory scattering approximation that accurately describes the transmitted (elastically scattered) wave, and still retains a mathematically invertible relation between the transmitted wave function and the specimen structure. It is shown that the path-integral method leads naturally to an invertible, higher-order, phase-object approximation, in addition to the usual kinematic approximation and the usual phase-object approximation. The higher-order phase-object approximation in turn leads to the noninvertible, multislice approximation of Cowley & Moodie, which had previously been derived by those authors from a semi-classical, physical-optics point of view.