Gevrey regularity of the Schrödinger equation

Assuming the initial condition has compact support, the solution to the Schrodinger equation with potential in R can be shown to be of class Gevrey-2 in time, even if the coefficients of the spatial differential operator are nonconstant. While our initial results assumed that the coefficients be C∞, an approach based on perturbation methods is used to extend the regularity result to systems with only bounded coefficients. The proof, however, is not a standard perturbation argument, since, if the differential operator with bounded coefficients is approximated by one with C∞ coefficients, the perturbation is not of lower order. This regularity of the solution has implications on exact controllability using boundary controls.