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

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 the problem of "mathematizing" it. We show that it holds exactly in the sense of distributions.

v2: Accepted Manuscript - Portugaliae Mathematica

References in corpus (1)

• Wave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects

Cited by in corpus (1)

• About the quantum Talbot effect on the sphere