An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics

Abstract

We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the standard WKB correction should be replaced by the solution to certain evolution equation.Comment: This is a preprint of an article whose final and definitive form has been published in Comm. Partial Differential Equations, available online at http://www.informaworld.co