Vanishing order of solutions to Schrodinger equation

TL;DR

This paper investigates the maximum order at which solutions to the Schrödinger equation can vanish when the potential is bounded, providing an upper bound on compact manifolds and demonstrating its sharpness.

Contribution

It establishes a sharp upper bound on the vanishing order of solutions to the Schrödinger equation with bounded potential on compact manifolds.

Findings

Derived an upper bound on vanishing order.

Proved the bound is sharp.

Applicable to solutions on compact manifolds.

Abstract

We study the possible vanishing order of solutions to Schrodinger equation in case the potential is a bounded function. We give an upper bound on compact manifold. We also show that this result is sharp.