On the classical limit of quantum mechanics and the threat of fundamental graininess and chaos to the correspondence principle

Details On the classical limit of quantum mechanics and the threat of fundamental graininess and chaos to the correspondence principle On the classical limit of quantum mechanics and the threat of fundamental graininess and chaos to the correspondence principle

2010-09-27

arxiv.org/abs/1009.5267v1

Physics

Quantum Physics

24 pages, 6 figures

Scientific paper

The aim of this paper is to review the classical limit of Quantum Mechanics and to precise the well known threat of chaos (and fundamental graininess) to the correspondence principle. We will introduce a formalism for this classical limit that allows ud find the surfaces defined by the constants of the motion in phase space. Then in the integrable case we will find the classical trajectories, and in the non-integrable one the fact that regular initial cells become "amoeboid-like". This deformations and their consequences can be considered as a threat to the correspondence principle. Essentially we present an analysis of the problem similar to the one of Omn\`es, but with a simpler mathematical structure.

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