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

The Talbot effect is usually modeled using the Helmholtz equation, but its main experimental features are captured by solution to free Schr\"odinger equation with Dirac comb as initial datum. This simplified description a consequence of paraxial approximation in geometric optics. However, it heuristic that not mathematically well justified, so K. I. Oskolkov raised problem "mathematizing" it. We show holds exactly sense distributions.