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

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

2011-07-05

arxiv.org/abs/1107.0790v1

Foundations of Physics and Probability (FPP6), V\"aj\"o : Sweden (2011)

Physics

Quantum Physics

14 pages, 2 figures

Scientific paper

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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