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Communication Dans Un Congrès Année : 2011

The two limits of the Schrödinger equation in the semi-classical approximation: discerned and non-discerned particles in classical mechanics

Résumé

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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Dates et versions

hal-00605920 , version 1 (04-07-2011)

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Michel Gondran, Alexandre Gondran. The two limits of the Schrödinger equation in the semi-classical approximation: discerned and non-discerned particles in classical mechanics. Foundations of Physics and Probability (FPP6), Jun 2011, Väjö, Sweden. ⟨hal-00605920⟩
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