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

TL;DR

This paper investigates the long-time behavior of 3D Schrödinger operators with specific potentials, showing that a new evolution equation replaces the standard WKB correction in asymptotic analysis.

Contribution

It introduces a novel evolution equation as the WKB correction for long-time asymptotics of Schrödinger dynamics with long-range potentials.

Findings

Existence of modified wave operators proved.

Standard WKB correction replaced by a new evolution equation.

Long-time asymptotics characterized for the specified Schrödinger operator.

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.