Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit (Q1282363)

The Wigner-transform techniques are applied to the analysis of difference methods for Schrödinger-type equations in the case of a small Planck constant. In this way, the authors are able to obtain sharp conditions on the spatial-temporal grid which guarantee convergence for average values of observables as the Planck constant lends to zero. Numerical sample computations and interpretations of the theory are given.