What question did this study set out to answer?

The aim is to enhance the understanding of quantum mechanics through a hydrodynamic framework using Madelung equations.

April 3, 2026Comptes Rendus Physique0 citationsOpen Access

On the hydrodynamic interpretation of non-relativistic quantum mechanics

Key Points

The aim is to enhance the understanding of quantum mechanics through a hydrodynamic framework using Madelung equations.
Derived equations from the Schrödinger equation using Madelung's principles.
Quantized a non-relativistic particle constrained to a surface wave with small slope.
Applied kinematic boundary conditions relating to Madelung velocity.
Established equivalence between Madelung equations and Euler equations for specific conditions.
Demonstrated the need for a distinct wave to satisfy the Schrödinger equation.
Presented a model where quantum potential replaces classical pressure in fluid dynamics.

Abstract

The Madelung equations express the Schrödinger equation as a continuity equation and modified Hamilton–Jacobi equation. These equations are equivalent to the Euler equations for a compressible, potential flow, when classical pressure per unit density is replaced by the quantum potential per unit mass. We extend this hydrodynamic interpretation by quantising a single, spinless, non-relativistic particle constrained to a surface wave with small slope. The wave is distinct from the wave function and, in order to reproduce the Schrödinger equation, it must satisfy the kinematic boundary condition for a free surface advected by twice the Madelung velocity field.

اسأل الذكاء الاصطناعي

Bookmark

View Full Paper