Uniqueness for the Schr\"odinger Equation on Graphs with Potential Vanishing at Infinity

TL;DR

This paper studies the uniqueness of solutions to the Schrödinger equation on infinite graphs with potentials that vanish at infinity, using weighted ℓ^p spaces to establish conditions for uniqueness.

Contribution

It introduces new criteria for the uniqueness of Schrödinger solutions on graphs with decaying potentials, extending previous results to more general graph structures.

Findings

Established uniqueness conditions for Schrödinger solutions with vanishing potentials.

Extended analysis to infinite graphs with potentials tending to zero at infinity.

Provided a framework for studying Schrödinger equations in weighted ℓ^p spaces.

Abstract

We investigate the uniqueness, in suitable weighted $\ell^p$ spaces, of solutions to the Schr\"odinger equation with a potential, posed on infinite graphs. The potential can tend to zero at infinite with a certain rate.