Quantum Chaos and Semiclassical Mechanics

This paper discusses the problem of finding and defining chaos in quantum mechanics. While chaotic time evolution appears to be ubiquitous in classical mechanics, it is apparently absent in quantum mechanics in part because for a bound, isolated quantum system, the evolution of its state is multiply periodic. This has led a number of investigators to search for semiclassical signatures of chaos. Here I am concerned with the status of semiclassical mechanics as a distinct third theory of the asymptotic domain between classical and quantum mechanics. I discuss in some detail the meaning of such crucial locutions as the " classical counterpart to a quantum system " and a quantum system ' s " underlying classical motion ". A proper elucidation of these concepts requires a semiclassical association between phase space surfaces and wave - functions. This significance of this association is discussed in some detail
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Gordon Belot & John Earman (1997). Chaos Out of Order: Quantum Mechanics, the Correspondence Principle and Chaos. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (2):147-182.
Alexandre Matzkin & Vanessa Nurock (2008). Classical and Bohmian Trajectories in Semiclassical Systems: Mismatch in Dynamics, Mismatch in Reality? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (1):17-40.

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