Time decay of scaling invariant Schroedinger equations on the plane

TL;DR

This paper establishes the optimal decay rate over time for solutions to the two-dimensional Schrödinger equation with a broad class of electromagnetic potentials that are invariant under scaling.

Contribution

It provides the first sharp L^1-L^{} decay estimates for 2D Schrödinger equations with general scaling critical electromagnetic potentials.

Findings

Proves sharp decay estimates for 2D Schrödinger equations with electromagnetic potentials.

Extends decay results to a broad class of scaling critical potentials.

Enhances understanding of dispersive properties in quantum mechanics models.

Abstract

We prove the sharp L^1-L^{\infty} time-decay estimate for the 2D-Schroedinger equation with a general family of scaling critical electromagnetic potentials.