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Bulletin of the American Physical Society

A Many-Body Extension to Madelung Quantum Hydrodynamics

David Michta, Frank R. Graziani, Gregory W. Hammett, Petros Tzeferacos

Published Nov 9, 2021• 0 citations
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According to Madelung, Bohm and Vigier, Wilhelm, Rosen and others, the original Schroedinger equation can be transformed into the hydrodynamical system of equations by using the so called Madelung ansatz. We derive in such quantum hydrodynamics, the non-relativistic and relativistic Strouhal number from the so called von Karman's vortex street. The relativistic derivation of this formula follows from the addition formula for velocities. The Strouhal friction tones are generated also during the motion of cosmic rays in relic photon sea, during the motion of bolids in atmosphere, during the Saturn rings motion in the relic black-body sea, during the motion of bodies in superfluid helium and so on.
It is shown that the Bohmian mechanics and the Madelung quantum hydrodynamics are different theories and the latter is a better ontological interpretation of quantum mechanics. A new stochastic interpretation of quantum mechanics is proposed, which is the background of the Madelung quantum hydrodynamics. Its relation to the complex mechanics is also explored. A new complex hydrodynamics is proposed, which eliminates completely the Bohm quantum potential. It describes the quantum evolution of the probability density by a convective diffusion with imaginary transport coefficients.