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      Superadiabatic transition histories in quantum molecular dynamics

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          Abstract

          We study the dynamics of a molecule's nuclear wave-function near an avoided crossing of two electronic energy levels, for one nuclear degree of freedom. We derive the general form of the Schroedinger equation in the n-th superadiabatic representation for all n, and give some partial results about the asymptotics for large n. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace, when a wave packet crosses the transition region. In the optimal superadiabatic representation, which we define, this component builds up monontonically. Finally, we give an explicit formula for the transition wave function away from the crossing, which is in excellent agreement with high precision numerical calculations.

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          Author and article information

          Journal
          2009-02-03
          Article
          0902.0646
          6d1bf23a-a137-4a61-9001-29400b671cfb

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          81V55, 34E20
          31 pages, 3 figures
          math-ph math.MP

          Mathematical physics,Mathematical & Computational physics
          Mathematical physics, Mathematical & Computational physics

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