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

Helmut Linde

Consider a closed curve of length $2\pi$ with curvature $\kappa (s)$ and the Schrödinger operator $H$ with ${\kappa }^2$ as the potential term. Let ${\lambda }_{\Gamma }$ be the lowest eigenvalue of $H$. The Ovals…