Quantum Potential from the Material Derivative of the Osmotic Velocity: A Two-Fluid Madelung Framework
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912677885902848 |
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| author | Simeonov, Lachezar |
| author_facet | Simeonov, Lachezar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Potential from the Material Derivative of the Osmotic Velocity: A Two-Fluid Madelung Framework Simeonov, Lachezar Quantum Physics 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. |
| title | Quantum Potential from the Material Derivative of the Osmotic Velocity: A Two-Fluid Madelung Framework |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.02868 |