Feynman Path Integral approach …

… to electron diffraction for one and two slits, analytical results

Schematic depiction of the apparatus with the source, the two-slits and the screen. We have represented four differents paths going through the slits, from the source to the screen. The dashed lines represent three classical paths and the thin dashed line a curved path. The Feynman path Integral formulation allows one to compute the propagator summing over all different paths

Mathieu Beau (STP-DIAS)
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).
It can thus be considered a complement to a recent article [S. Fraboni et al, Am. Journ. Phys.  79 (6), 615–618 (2011)] about the two- and three slit problem from an experimental/computational point of view.
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….
Read more: http://arxiv.org/pdf