Development and numerical analysis of "black-box" counterpropagating wave algorithm for exact quantum scattering calculations

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In a recent series of papers,1-3 a bipolar counter-propagating wave decomposition, Ψ = Ψ + + Ψ -, was presented for stationary bound states Ψ of the one-dimensional Schrödinger equation, such that the components Ψ± approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Ψ has many nodes, or is wildly oscillatory. In this paper, the earlier results are used to construct an universal "black-box" algorithm, numerically robust, stable and efficient, for computing accurate scattering quantities of any quantum dynamical system in one degree of freedom.

Original languageEnglish
Pages (from-to)99-125
Number of pages27
JournalJournal of Theoretical and Computational Chemistry
Issue number1
StatePublished - Mar 2007



  • Bohmian mechanics
  • Partial differential equations
  • Quantum trajectory methods
  • Reactive scattering

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