Separation for Schrödinger operators. A counterexample to Simon's conjecture

Abstract

We construct, for every $d\ge 5$, a nonnegative radial potential $V\in L_{\mathrm{loc}}^{\infty }({\mathbb{R}}^d\setminus \{0\})\cap L^1({\mathbb{R}}^d)$ for which $V(-\Delta \dotplus V{)}^{-1}$ is not bounded on $L^2({\mathbb{R}}^d)$.

6 pages. Comments are welcome