Light and matter diffraction from the unified viewpoint of Feynman's Sum of all Paths

Abstract

In this work, we present a pedagogical strategy to describe the diffraction phenomenon based on a didactic adaptation of the Feynman's path integrals method, which uses only high school mathematics. The advantage of our approach is that it allows to describe the diffraction in a fully quantum context, where superposition and probabilistic aspects emerge naturally. Our method is based on a time-independent formulation, which allows modelling the phenomenon in geometric terms and trajectories in real space, which is an advantage from the didactic point of view. A distinctive aspect of our work is the description of the series of transformations and didactic transpositions of the fundamental equations that give rise to a common quantum framework for light and matter. This is something that is usually masked by the common use, and that to our knowledge has not been emphasized enough in a unified way. Finally, the role of the superposition of nonclassical paths and their didactic potential are briefly mentioned.