Quantitative uniqueness for Schr\"odinger operator

TL;DR

This paper establishes a precise upper limit on how rapidly solutions to the Schrödinger equation can vanish, assuming the potential is continuously differentiable on a smooth compact manifold.

Contribution

It provides a sharp upper bound on the vanishing order of Schrödinger solutions with $ ext{C}^1$ potentials on smooth compact manifolds, advancing understanding of solution behavior.

Findings

Sharp upper bound on vanishing order established

Results applicable to $ ext{C}^1$ potentials on smooth manifolds

Enhances understanding of Schrödinger solution properties

Abstract

We give a sharp upper bound on the vanishing order of solutions to Schr\"odinger equation, in the case that the potential is of class $\mathcal{C}^1$ on a smooth compact manifold.