Feynman Path Integral approach to electron diffraction for one and two slits, analytical results

TL;DR

This paper provides an analytical solution to electron diffraction through one and two slits using Feynman's path integral approach, offering exact formulas and approximations to aid understanding of quantum interference.

Contribution

It introduces an exact analytical solution for electron diffraction problems using Feynman's path integral method, serving as a pedagogical resource.

Findings

Exact formulas for electron diffraction patterns

Various approximations to interpret results

Educational insights into Feynman's quantum mechanics formulation

Abstract

In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we exhibit various approximations of the electron distribution which facilitate the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could therefore also serve as an interesting pedagogical introduction to Feynman's formulation of quantum mechanics for university students dealing with the foundations of quantum mechanics.