TY - JOUR
T1 - Development and numerical analysis of "black-box" counterpropagating wave algorithm for exact quantum scattering calculations
AU - Poirier, Bill
N1 - Funding Information:
This work was supported by an award from The Welch Foundation (D-1523). Corey Trahan is acknowledged for performing some of the preliminary numerical investigations.
PY - 2007/3
Y1 - 2007/3
N2 - 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.
AB - 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.
KW - Bohmian mechanics
KW - Partial differential equations
KW - Quantum trajectory methods
KW - Reactive scattering
UR - http://www.scopus.com/inward/record.url?scp=34047269254&partnerID=8YFLogxK
U2 - 10.1142/S0219633607002836
DO - 10.1142/S0219633607002836
M3 - Article
AN - SCOPUS:34047269254
VL - 6
SP - 99
EP - 125
JO - Journal of Theoretical and Computational Chemistry
JF - Journal of Theoretical and Computational Chemistry
SN - 0219-6336
IS - 1
ER -