Application of the spectral element method to the solution of the multichannel Schrödinger equation
arXiv:1705.04102
Abstract
We apply the spectral element method to the determination of scattering and bound states of the multichannel Schrödinger equation. In our approach the reaction coordinate is discretized on a grid of points whereas the internal coordinates are described by either purely diabatic or locally diabatic (diabatic-by-sector) bases. Bound levels and scattering matrix elements are determined with spectral accuracy using relatively small numbers of points. The scattering problem is cast as a linear system solved using state-of-the-art sparse matrix non iterative packages. Boundary conditions can be imposed so to compute a single column of the matrix solution. A comparison with log-derivative propagators customarily used in molecular physics is performed. The same discretization scheme can also be applied to bound levels that are computed using direct scalable sparse-matrix solvers.
24 pages, 5 figures