  Consider a solution $u$ to $\Delta u +Vu=0$ on $\mathbb{R}^2$, where $V$ is
real-valued, measurable and $|V|\leq 1$. If $|u(x)| \leq \exp(-C |x|
\log^{1/2}|x|)$, $|x|>2$, where $C$ is a sufficiently large absolute constant,
then $u\equiv 0$.
