A Quantum Mechanics Treatment of Electron Diffraction by a Slit

Abstract

The diffraction of particles (electrons, neutrons, protons, atoms) by slits is a phenomenon that should be treated in the frame of quantum mechanics (QM) by solving the Schrodinger equation. However in most cases the Huygens principle and/or the Kirchhoff and Fresnel formalisms have been used. An approach to apply QM to the diffraction of particles by a single or double slit was reported in reference [1]. However they proposal can only be applied when the opaque plate containing the slits has a negligible thickness. More recently in another report [2] the diffraction of neutrons by slits was analyzed. These authors considered the slit as an infinite potential well. The particles when traversing the slit must occupy the quantum states due to this well potential. Nevertheless, the authors fail giving a complete QM description as they applied the classic Kirchhoff formulation at the exit plane of the slit.