Analytic wave front set for solutions to Schroedinger equation

This paper is a continuation of a previous paper by the same authors, where an analytic smoothing effect was proved for long-range type perturbations of the Laplacian $H_0$ on ${\text{re}}^n$. In this paper, we consider short-range type perturbations $H$ of the Laplacian on ${\text{re}}^n$, and we characterize the analytic wave front set of the solution to the Schr"odinger equation: $e^{-itH}f$, in terms of that of the free solution: $e^{-it{H}_0}f$, for $t<0$ in the forward nontrapping region. The same result holds for $t>0$ in the backward nontrapping region. This result is an analytic analogue of results by Hassel and Wunsch and Nakamura.