Istituto di Matematica Applicata e Tecnologie Informatiche     
Markowich P. A., Pietra P., Pohl C. Semiclassical analysis of discretizations of Schroedinger-type equations. Preprint ercim.cnr.ian//1997-1070, 1997.
We apply Wigner-transform techniques to the analysis of difference methods for the Schroedinger equation in the case of a small scaled Planck constant. In this way we are able to obtain sharp conditions on the spatial-temporal grid which guarantee convergence for average values of observables as the Planck constant tends to zero. The theory developed in this paper is not based on local and global error estimates and does not depend on whether caustics develop or not.
Subject Schroedinger equations, Wigner-transform

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