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Semiclassical Mechanics with Molecular Applications$
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M. S. Child

Print publication date: 2014

Print ISBN-13: 9780199672981

Published to Oxford Scholarship Online: October 2014

DOI: 10.1093/acprof:oso/9780199672981.001.0001

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Non-separable bound motion

Non-separable bound motion

(p.142) 7 Non-separable bound motion
Semiclassical Mechanics with Molecular Applications

M. S. Child

Oxford University Press

Non-separable bound states in the regular regime lie on f–dimensional invariant tori in the 2f–dimensional phase space. Actions and quantum numbers are fixed by the areas of f topologically distinct cuts through the torus. Poincaré sections are useful in revealing bifurcations in the torus structure, as for example in the transition from normal to local vibrational motion. Various quantization schemes include EBK and classical perturbation theory, adiabatic switching and Fourier representations of the torus. Finally, periodic-orbit-based expressions are given for the densities of states of both regular and chaotic systems. The observation of periodic ‘scars’ on the wavefunction is of particular interest.

Keywords:   invariant torus, regular, chaotic, EBK, adiabatic switching, density of states, periodic orbit, scars

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