### 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.

Original language | English (US) |
---|---|

Article number | 18 |

Journal | Fluids |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2016 |

### Fingerprint

### Keywords

- Madelung model
- Mass and momentum transfer
- Navier-Stokes equations
- Quantum mechanics
- Schrödinger equation

### ASJC Scopus subject areas

- Mechanical Engineering
- Fluid Flow and Transfer Processes
- Condensed Matter Physics

### Cite this

**Rendering the Navier-Stokes equations for a compressible fluid into the Schrödinger equation for quantum mechanics.** / Vadasz, Peter.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Rendering the Navier-Stokes equations for a compressible fluid into the Schrödinger equation for quantum mechanics

AU - Vadasz, Peter

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

AB - 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.

KW - Madelung model

KW - Mass and momentum transfer

KW - Navier-Stokes equations

KW - Quantum mechanics

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85052057461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052057461&partnerID=8YFLogxK

U2 - 10.3390/fluids1020018

DO - 10.3390/fluids1020018

M3 - Article

VL - 1

JO - Fluids

JF - Fluids

SN - 2311-5521

IS - 2

M1 - 18

ER -