The Equations of Fluid Dynamics in Mechanics, Probability, and Quantum Mechanics: A Confrontation

Joseph Louis Bass

James Lill, M. I. Haftel, G. H. Herling

A newly derive set of quantum fluid dynamical equations appropriate for the description of mixed state dynamics is presented. Based essentially on moments of the Wigner function, the theory presented here uses an expansion of the pseudodistribution function in conjunction with a renormalization technique to obtain a semiclassical approximation for the dynamics of the probability, probability current, and energy densities. Particularly simple equations, ideal fluid dynamics with a nonlocal potential, result from using a local Maxwellian ansatz for the Wigner function. Further, the transformed potential may be easily computed from the fields being convected. Analogies with classical kinetic theory and fluid dynamics are exploited whenever possible.

L. J. F. Broer

Framework for QFD in 3-D Space .............................................................188 12.5 Quantum Fluid Dynamical Equations within a Density Functional Framework..................................................................................................191 12.6 Miscellaneous Aspects of the Quantum Fluid Dynamical Approach .........193 12.7 Concluding Remarks...................................................................................194 Acknowledgments..................................................................................................194 Bibliography ..........................................................................................................194 The concepts of quantum mechanics (QM) are so radically different from those of classical mechanics that soon after Schrödinger proposed the concept of quantum mechanical wavefunction, there were attempts to provide a classical interpretation of QM. In fact, the success of Madelung [1] in transforming the Schrödinger equation into a pair of hydrodynamical equations consisting of the continuity equation and an Euler type equation of hydrodynamics, giving birth to so-called quantum fluid dynamics (QFD) [2-5], in 1926, itself is testimony to the strong urge to have a classical interpretation of the strange world of QM. The concept was resurrected with full vigor more than 25 years later through the pioneering works of Bohm [6] and Takabayashi [7]. In the meantime, Wigner [8] introduced, in 1932, the concept

Hiromoto Susawa

Germano Resconi, Santanu Kumar Patro, Amrit Šorli

In this paper, we present the quantum mechanics as a reactive system. To show this, “holography” is introduced as a reactive system. Illumination of the object and reference beam create sources (hologram) that are activated by the same reference beam, which is reacted in a way to produce the image. Controlled chemical system reacts to the external or internal change generated new sources (chemical product) that diffuse in the body environment, and establishes a new equilibrium. The droplets bouncing on a vertical vibrating fluid bath that simulates the main quantum phenomena is a reactive system between droplets and vibrating fluid. It is shown that quantum mechanics is a probabilistic reactive system between quantum potential and pseudo kinetic energy in which an integral is the Fisher information. Information and probability are the key points in quantum mechanics. Quantum mechanics can be built by only the probability normalization properties and associated information without assuming any other hypothesis. With joint probability and Fisher information by Euler Lagrange equation, we can find the quantum potential and the continuity equation. With only probability approach, it is possible to give a meaning to the Schrodinger equation without any thermo-dynamical model of quantum mechanics. The reactive system can be denoted as a morphogenetic system where the form is generated by some designed rules or properties.