A note on local behavior of eigenfunctions of the Schr\"odinger operator

TL;DR

This paper investigates the local behavior of eigenfunctions of the Schrödinger operator, demonstrating that under certain potential conditions, these eigenfunctions must change sign near some point in space.

Contribution

It provides a new insight into the sign-changing behavior of eigenfunctions locally, under specific assumptions on the potential.

Findings

Eigenfunctions change sign near some point in bR^n

Sign-changing behavior depends on potential assumptions

Provides conditions for local sign change of eigenfunctions

Abstract

We show that a real eigenfunction of the Schr\"odinger operator changes sign near some point in $\mathbb{R}^n$ under a suitable assumption on the potential.