Eulerian and Newtonian dynamics of quantum particles

TL;DR

This paper derives quantum mechanics equations from classical hydrodynamics, showing quantum behavior as an ensemble of oscillating classical particles, and proposes a classical model for quantum motion.

Contribution

It introduces a hydrodynamic framework that derives the Schrödinger equation from classical equations and models quantum systems as oscillating classical ensembles.

Findings

Quantum systems can be modeled as inviscid gases with oscillating temperature.

Average quantum motion corresponds to classical hydrodynamic equations.

A classical model for quantum motion consistent with the hydrodynamic approach.

Abstract

We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and described by the Schrodinger equation, can be considered as an inviscid gas obeying the ideal gas law with quickly oscillating sign-alternating temperature. This statistical ensemble performs the complex movements consisting of smooth average movement and fast oscillations. It is shown that average movements of statistical ensemble are described by Schrodinger equation. A model of quantum motion within the limits of classical mechanics which corresponds to the considered hydrodynamic system is suggested.