  We apply the spectral element method to the determination of scattering and
bound states of the multichannel Schr\"odinger 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.
