By R. Blümel, W. P. Reinhardt

The examine of chaos is this day the most energetic and prolific components in atomic physics. This booklet describes the manifestations of chaos in atoms and molecules, and is an advent to this attention-grabbing sector. the 1st a part of the ebook bargains with the speculation and rules of classical chaos, that are then utilized to genuine atomic and molecular physics platforms within the moment a part of the publication. The ebook covers microwave-driven floor nation electrons, the hydrogen atom in a powerful microwave box, the kicked hydrogen atom, chaotic scattering with CsI molecules and the helium atom. The booklet includes many diagrams and a close reference checklist.

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Is not rational. The proof was known to the ancient Greeks: assume \/2 is rational. Then, it can be written as y/2 — n/m where n and ra are integers and relatively prime. Squaring this relation we get n 2 = 2m2. This means that n2 contains a factor 2. But if n 2 contains a factor 2, so does n. Therefore, we write n2 = 4p, where p is another integer. Thus, m2 = 2p. Using the same argument as before, m contains a factor 2. But this contradicts the assumption that n and m are relatively prime. Thus we proved that \/2 is not rational.

The second reason for the initial low impact of Poincare's work was the advent of quantum mechanics. Quantum mechanics is such a successful theory that the focus of attention quickly shifted away from (nonlinear) dynamical systems theory to the solution of (linear) quantum problems in atomic, molecular, nuclear and solid state physics. Quantum mechanics, of course, raises its own issues of determinism and predictability. The problem is not so much with the "machinery" of quantum mechanics, which produces correct results whenever applied to microscopic systems.

Schroeder (1991), p. 161). Specifying an initial condition with an infinite number of words or prescriptions again makes no physical sense. Accordingly, most numbers in [0,1] do not qualify as physical initial conditions which could reasonably be specified. What happens if a chaotic mechanical system starts with such an unspecifiable initial condition? We will see in Chapter 2 that the resulting motion of the system, although deterministic, is then random. Fig. 9 hints at the complexity which can follow.

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