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arXiv · 0803.0309

Development and Numerical Analysis of "Black-box" Counterpropagating Wave Algorithm for Exact Quantum Scattering Calculations

Bill Poirier
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Abstract

In a recent series of papers [J. Chem. Phys. 121 4501 (2004), J. Chem. Phys. 124 034115 (2006), J. Chem. Phys. 124 034116 (2006)] a bipolar counter-propagating wave decomposition, Psi = Psi+ + Psi-, was presented for stationary bound states Psi of the one-dimensional Shrodinger equation, such that the components Psi+- approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. In this paper, the earlier results are used to construct a universal ``black-box'' algorithm, numerically robust, stable and efficient, for computing accurate scattering quantities of any quantum dynamical system in one degree of freedom.

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Bill Poirier. 2008-03-03. Development and Numerical Analysis of "Black-box" Counterpropagating Wave Algorithm for Exact Quantum Scattering Calculations. https://arxiv.org/abs/0803.0309

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