Quantum Particle Statistics in Classical Shallow Water Waves

TL;DR

This paper introduces a hydrodynamic analogy linking shallow water waves to quantum particles, revealing classical interpretations of quantum statistics and dynamics through wave-particle interactions.

Contribution

It establishes a novel classical analogy between shallow water waves and quantum particles, providing insights into quantum statistics and state transitions.

Findings

Water wave dynamics mimic quantum particle behavior

Classical interpretation of Born's rule demonstrated

Mechanism for transition between quantum states proposed

Abstract

We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show that when locally oscillating particles are guided by real wave gradients, particles may exhibit trajectories of alternating periodic or chaotic dynamics while increasing the wave potential. The particle probability distribution function of this analogy reveals the quantum statistics of the standard solutions of the Schr\"odinger equation and thus manifests as a classical deterministic interpretation of Born's rule. Finally, a classical mechanism for the transition between quasi-stationary states is proposed.