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arXiv · 1107.0790

The two limits of the Schr\"odinger equation in the semi-classical approximation: discerned and non-discerned particles in classical mechanics

Michel Gondran·Alexandre Gondran
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Abstract

We study, in the semi-classical approximation, the convergence of the quantum density and the quantum action, solutions to the Madelung equations, when the Planck constant h tends to 0. We find two different solutions which depend to the initial density . In the first case where the initial quantum density is a classical density rho_0(x), the quantum density and the quantum action converge to a classical action and a classical density which satisfy the statistical Hamilton-Jacobi equations. These are the equations of a set of classical particles whose initial positions are known only by the density rho_0(x). In the second case where initial density

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Michel Gondran, Alexandre Gondran. 2011-07-05. The two limits of the Schr\"odinger equation in the semi-classical approximation: discerned and non-discerned particles in classical mechanics. https://doi.org/10.1063/1.3688959

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