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.

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.com