RESUMEN

The time-dependent Schr¨odinger equation is discretized in space by a sparse gris pseudospectral method. The Strang splitting for the resulting evolutionary problem features first or second order convergence in time, depending on the smoothness of the potential and of the inicial data. In contrast to the full grid case, where the frequency domain is the working place, the Prof. of the sufficient conditions for the convergence is done in the space realm.