An improved bound for the ground state of a Schrödinger operator on a loop

Helmut Linde

Consider a closed curve of length $2\ddot{I}€$ with curvature $\hat{I}º(s)$ and the Schrödinger operator $H$ with $\hat{I}{º}^2$ as the potential term. Let $\hat{I}{»}_{\hat{I}}“$ be the lowest eigenvalue of $H$. The…