dc.creator Child, M. S. en_US dc.date.accessioned 2006-06-15T20:16:41Z dc.date.available 2006-06-15T20:16:41Z dc.date.issued 2001 en_US dc.identifier 2001-WE-01 en_US dc.identifier.uri http://hdl.handle.net/1811/20277 dc.description $^{a}$M S Child in `Computational Molecular Spectroscopy', Eds P Jensen and P R Bunker (Wiley, 2000) $^{b}$M S Child, T Weston and J Tennyson, Mol Phys, 96, 371 (1999) en_US dc.description Author Institution: Dept. of Chemistry, Physical and Theoretical Chemistry Laboratory en_US dc.description.abstract It is well known that certain wavefunctions follow the shapes of classical trajectories close to stable classical periodic orbits. This paper concerns a deeper relationship between the organization of quantum mechanical eigenvalues and the number and types of classical periodic orbits, illustrated by reference to effective spectroscopic $Hamiltonians^{a}$. The simplest cases are perhaps the local stretching states of $H_{2}O$ or $H_{2}S$, for which one sees a pattern of progressively close local mode doublets at energies below the separatrix associated with an unstable orbit, and an increasingly regular pattern of energy separations above it. Similar, but more complex behavior is found in highly excited Fermi resonance polyads. There is also a classically related generic pattern (termed quantum $monodromy^{b}$) in the level structures arising from any cylindrically symmetric saddle point. Examples will be given for the bent to linear states of $H_{2}O$, pendular states of dipolar molecules in electric fields and highly excited Fermi resonant states of $CO_{2}$. en_US dc.format.extent 527834 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title QUANTUM LEVEL STRUCTURES AND NON-LINEAR CLASSICAL DYNAMICS en_US dc.type article en_US
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