Quantum hydrodynamics, Wigner transforms, the classical limit

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Abstract
We analyse the classical limit of the quantum hydrodynamic equations as the Planck constant tends to zero. The equations have the form of an Euler system with a constant pressure and a dispersive regularisation term, which (formally) tends to zero in the classical limit. The main tool of the analysis is the exploitation of a kinetic equation, which lies behind the quantum hydrodynamic system. The presented analysis can also be interpreted as an alternative approach to the geometrical optics (WKB)-analysis of the Schrödinger equation.

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