  Scattering states with LEED asymptotics are calculated for a general
non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier
and image potential part. The latter applies especially to the case of low
lying conduction bands. The wave function is described with a reciprocal
lattice representation parallel to the surface and a discretization of the real
space perpendicular to the surface. The Schroedinger equation leads to a system
of linear one-dimensional equations. The asymptotic boundary value problem is
confined via the quantum transmitting boundary method to a finite interval. The
solutions are obtained basing on a multigrid technique which yields a fast and
reliable algorithm. The influence of the boundary conditions, the accuracy and
the rate of convergence with several solvers are discussed. The resulting
charge densities are investigated.
