Application of the spectral element method to the solution of the multichannel Schroedinger equation

Andrea Simoni (1) , Alexandra Viel (1) , Jean-Michel Launay (1)

1 IPR - Institut de Physique de Rennes

We apply the spectral element method to the determination of scattering and bound states of themultichannel Schrodinger equation. In our approach, the reaction coordinate is discretized on a gridof 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 spectralaccuracy using relatively small number of points. The scattering problem is cast as a linear sys-tem solved using state-of-the-art sparse matrix non-iterative packages. Boundary conditions can beimposed so as to compute a single column of the matrix solution. A comparison with log-derivativepropagators customarily used in molecular physics is performed. The same discretization scheme canalso be applied to bound levels that are computed using direct scalable sparse-matrix solvers.

Mots clés: Spectral element methods; Cold and ultra-cold collisions; Molecular physics; Quantum dynamics; Atomic and molecular collisions

Domaines: Physique [physics]

Andrea Simoni, Alexandra Viel, Jean-Michel Launay. Application of the spectral element method to the solution of the multichannel Schroedinger equation. Journal of Chemical Physics, 2017, 146 (24), pp.244106-1-9. ⟨10.1063/1.4987026⟩. ⟨hal-01551686⟩