Abstract
Hydrodynamics and quantum mechanics have many elements in common, as the density field and velocity fields are common variables that can be constructed in both descriptions. Starting with the Schroedinger equation and the Klein-Gordon for a single particle in hydrodynamical form, we examine the basic assumptions under which a quantum system of particles interacting through their mean fields can be described by hydrodynamics.
Highlights
Hydrodynamics has applications in many areas of physics, for both finite and infinite systems [1]-[17]
We are interested in hydrodynamics of quantum systems in which particles obey quantum mechanics, as for example, in
It is useful to examine to what extent quantum mechanics for the motion of a single particle may be a part of the foundation for a hydrodynamical description of a quantum many-body system
Summary
Hydrodynamics has applications in many areas of physics, for both finite and infinite systems [1]-[17]. There are finite-size quantum shell effects that arise from the quantization of single-particle states and these quantum effects exert great influences on the static nuclear geometrical configurations at their local energy minima The interplay of both the classical bulk liquid-drop behavior and the quantum single-particle effect has led to rich phenomena of many local geometrical configurations built on top of a general underlying liquid-drop background ("Funny Hills" as described in [18]). It is useful to examine to what extent quantum mechanics for the motion of a single particle may be a part of the foundation for a hydrodynamical description of a quantum many-body system
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