Quantum Potential from the Material Derivative of the Osmotic Velocity: A Two-Fluid Madelung Framework

• URL: http://arxiv.org/abs/2509.02868v2
• Date: Thu, 30 Oct 2025 08:53:22 GMT
• Title: Quantum Potential from the Material Derivative of the Osmotic Velocity: A Two-Fluid Madelung Framework
• Authors: Lachezar Simeonov,
• Abstract summary: We derive the quantum potential directly from the material derivative of the osmotic velocity.<n>We formulate a two-fluid model that reproduces the Madelung equations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive the quantum potential directly from the material derivative of the osmotic velocity and formulate a two-fluid model that reproduces the Madelung equations. Interactions between the fluids are included but remain secondary. The framework is generalized to incorporate electromagnetic fields, yielding self-consistent description of both the Schrodinger and Klein-Gordon equations. Extenstion to the relativistic Klein-Gordon case demonstrates the model's flexibility and applicability to spinless relativistic quantum systems. This approach unifies hydrodynamic, kinematic, and electromagnetic perspectives, providing a clear physical interpretation of quantum potentials and forces and offering a versatile platform for modeling complex quantum systems in both non-relativistic and relativistic regimes.

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