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Open Quantum Systems Decoherence
On the hydrodynamic interpretation of non-relativistic quantum mechanics
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Authors: James Day
Year
2026
Paper ID
45170
Status
Peer-reviewed
Abstract Read
~2 min
Abstract Words
100
Citations
N/A
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.
Why This Paper Matters
- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
- It adds a 2026 reference point for readers tracking recent quantum research.
- The Madelung equations express the Schrödinger equation as a continuity equation and modified Hamilton–Jacobi equation.
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