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Fluids 2016, 1(2), 18; doi:10.3390/fluids1020018

Rendering the Navier–Stokes Equations for a Compressible Fluid into the Schrödinger Equation for Quantum Mechanics

Department of Mechanical Engineering, Northern Arizona University, P.O. Box 15600, Flagstaff, AZ 86001, USA
Academic Editor: Rama S.R. Gorla
Received: 2 May 2016 / Revised: 2 June 2016 / Accepted: 6 June 2016 / Published: 13 June 2016
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Abstract

The mass and momentum transfer phenomena in a compressible fluid represented by the Navier–Stokes equations are shown to convert into the Schrödinger equation for quantum mechanics. The complete Navier–Stokes equations render into an extended generalized version of Schrödinger equation. These results complement the Madelung’s (Zeitschrift für Physik 40 (3–4), pp. 322–326, 1926–1927) derivations that show how Schrödinger’s equation in quantum mechanics can be converted into the Euler equations for irrotational compressible flow. The theoretical results presented here join the classical Madelung paper to suggest the possibility that quantum effects at sub-atomic levels deal with a compressible fluid susceptible to wave propagation, rather than a particle. The link between such a fluid and the “quantum particle” is under current investigation. View Full-Text
Keywords: Navier–Stokes equations; mass and momentum transfer; Schrödinger equation; quantum mechanics; Madelung model Navier–Stokes equations; mass and momentum transfer; Schrödinger equation; quantum mechanics; Madelung model
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Vadasz, P. Rendering the Navier–Stokes Equations for a Compressible Fluid into the Schrödinger Equation for Quantum Mechanics. Fluids 2016, 1, 18.

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