Fourier Optics and Time Evolution of De Broglie Wave Packets

TL;DR

This paper demonstrates that under the Fresnel approximation, optical diffraction and interference can be understood as the time evolution of a wave packet, linking classical optics phenomena with quantum wave mechanics.

Contribution

It establishes a theoretical connection between wave packet spreading in quantum mechanics and optical diffraction patterns under the Fresnel approximation.

Findings

Diffraction patterns correspond to wave packet spreading over time.

The time for wave packet evolution matches the quantum crossing time of the optical setup.

Provides a new perspective for wave mechanics and quantum physics education.

Abstract

We prove that, under the condition of validity of the Fresnel approximation, diffraction and interference for a wave traveling in the z-direction may be described in terms of the spreading in time of the transverse (x,y)-wave packet. The time required for the evolved wave packet to yield identical patterns as given by standard optics corresponds to the time for the quantum to cross the optical apparatus. This point of view may provide interesting cues in wave mechanics and quantum physics education.