We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (in which the constant is no longer reduced to the standard quantum constant h̄) is equivalent to a generalized Schrödinger equation. Then we show that, even in the case of the presence of vorticity, it is also possible to ...

A quantum fluid dynamic(QFD) control formulation is presented for optimally manipulating atomic and molecular systems. In QFD the control quantum system is expressed in terms of the probability density ρ and the quantum current j. This choice of variables is motivated by the generally expected slowly varying spatial-temporal dependence of the fluid dynamical variables. The QFD approach is illus...

The quantization of gravity coupled to a perfect fluid model leads to a Schrödingerlike equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state p = αρ; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scal...

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) d...

We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (depending on a constant which may be different from the standard quantum constant h̄) is equivalent to a generalized Schrödinger equation for a ‘wavefunction’ whose modulus squared yields the fluid density. Then we show th...