The Talbot effect as the fundamental solution to the free Schr\"odinger equation
Analysis of PDEs
2021-09-02 v2 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
The Talbot effect is usually modeled using the Helmholtz equation, but its main experimental features are captured by the solution to the free Schr\"odinger equation with the Dirac comb as initial datum. This simplified description is a consequence of the paraxial approximation in geometric optics. However, it is a heuristic approximation that is not mathematically well justified, so K. I. Oskolkov raised the problem of "mathematizing" it. We show that it holds exactly in the sense of distributions.
Cite
@article{arxiv.2102.11962,
title = {The Talbot effect as the fundamental solution to the free Schr\"odinger equation},
author = {Daniel Eceizabarrena},
journal= {arXiv preprint arXiv:2102.11962},
year = {2021}
}
Comments
v2: Accepted Manuscript - Portugaliae Mathematica