%0 Journal Article
%T Schr£żdinger Operators With $A_\infty$ Potentials
%A Andrew Raich
%A Michael Tinker
%J Mathematics
%D 2015
%I arXiv
%X We study the heat kernel $p(x,y,t)$ associated to the real Schr\"odinger operator $H = -\Delta + V$ on $L^2(\mathbb{R}^n)$, $n \geq 1$. Our main result is a pointwise upper bound on $p$ when the potential $V \in A_\infty$. In the case that $V\in RH_\infty$, we also prove a lower bound. Additionally, we compute $p$ explicitly when $V$ is a quadratic polynomial.
%U http://arxiv.org/abs/1508.07150v1