Is Fresnel Optics Quantum Mechanics in Phase Space?

TL;DR

This paper explores a potential deep connection between Wigner's quantum phase space distribution and classical Fresnel optics, suggesting a novel perspective on the relationship between quantum mechanics and classical wave optics.

Contribution

It proposes a conjecture linking quantum phase space distributions with classical Fresnel optics, offering a new conceptual framework.

Findings

Establishes a theoretical link between Wigner functions and Fresnel diffraction patterns

Provides mathematical formulation supporting the conjecture

Suggests implications for understanding quantum-classical correspondence

Abstract

We formulate and argue in favor of the following conjecture: There exists an intimate connection between Wigner's quantum mechanical phase space distribution function and classical Fresnel optics.