# The Talbot effect as the fundamental solution to the free Schrödinger equation

### Daniel Eceizabarrena

University of Massachusetts Amherst, USA

## Abstract

The Talbot effect is usually modeled using the Helmholtz equation, but its main experimental features are captured by the solution to the free Schrödinger 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 in [20] the problem of ‘‘mathematizing’’ it. We show that it holds exactly in the sense of distributions.

## Cite this article

Daniel Eceizabarrena, The Talbot effect as the fundamental solution to the free Schrödinger equation. Port. Math. 78 (2021), no. 2, pp. 233–253

DOI 10.4171/PM/2068