Abstract
We study the classical limit of the dynamics of (i) three simple quantum systems, and (ii) a semi-quantum one based on the nonlinear coupling between two subsystems: a classical and a quantum one. The investigation revolves around a particular motion-invariant, I, closely related to the uncertainty principle. We also revisit the classical treatment of these systems and find that the classical limit of the three quantum systems not only yields the same results of the purely classical treatment, but that the limiting process itself exhibits common characteristics in the three cases. This classical limit is determined by the relationship between I and the total energy. These features are also exhibited in the semi-quantum instance, although a novel characteristic is detected here: an abrupt transition between different regimes. The workings of an adequate variable that expresses the relationship between I and the energy allows for some insights into the features of the “classical–quantum transition”.
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