On the hydrodynamic interpretation of non-relativistic quantum mechanics
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.
Fields of Study & Subjects
Quantum Mechanics and Non-Hermitian Physics
Quantum chaos and dynamical systems
Quantum Mechanics and Applications
Publication details
- Journal / source
- Comptes Rendus Physique
- Publisher
- MathDoc/Centre Mersenne
- Volume
- 27
- Issue
- G1
- Pages
- 183–189
- Publication date
- 2 April 2026
- Language
- EN