On minimal support properties of solutions of Schr\"odinger equations

TL;DR

This paper investigates the minimal support properties of solutions to Schrödinger equations, improving conditions on the potential and deriving new results on unique continuation, which are crucial for understanding the behavior of quantum systems.

Contribution

The paper advances the understanding of support properties of Schrödinger solutions by refining potential conditions and establishing new unique continuation results.

Findings

Improved conditions on the potential for minimal support of solutions.

Established new unique continuation results for Schrödinger operators.

Enhanced understanding of solution support constraints in quantum mechanics.

Abstract

In this paper we obtain minimal support properties of solutions of Schr\"odinger equations. We improve previously known conditions on the potential for which the measure of the support of solutions cannot be too small. We also use these properties to obtain some new results on unique continuation for the Schr\"odinger operator.