A TIMEADAPTIVE AND SPACEADAPTIVE ALGORITHM FOR THE LINEAR TIME-DEPENDENT SCHRODINGER-EQUATION

We prove an a posteriori error estimate for the linear time-dependent Schrodinger equation in R(N). From this, we derive a residual based lo cal error estimator that allows us to adjust the mesh and the time ste p size in order to obtain a numerical solution with a prescribed accur acy. As a special feature, the error estimator controls localization a nd size of the finite computational domain in each time step. An algor ithm is described to compute this solution and numerical results in on e space dimension are included.