A Theorem of Paley-Wiener Type for Schr\"odinger Evolutions

TL;DR

This paper establishes unique continuation principles for solutions of time-dependent Schr"odinger equations, extending Paley-Wiener type uncertainty principles to a broad class of semi-linear Schr"odinger equations.

Contribution

It introduces new unique continuation results for Schr"odinger evolutions with time-dependent potentials, generalizing Paley-Wiener type uncertainty principles.

Findings

Unique continuation principles proven for Schr"odinger equations with time-dependent potentials

Extension of Paley-Wiener type uncertainty principles to semi-linear Schr"odinger equations

Results applicable to a large class of Schr"odinger evolutions

Abstract

We prove unique continuation principles for solutions of evolution Schr\"odinger equations with time dependent potentials. These correspond to uncertainly principles of Paley-Wiener type for the Fourier transform. Our results extends to a large class of semi-linear Schr\"odinger equation.