Lower bounds for the spinless Salpeter equation

Abstract

We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schr\"odinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts are in $L^p(\R^n)$ for some $p>n$ ($n=1$ or 3). An extension to confining potentials, which are not in $L^p(\R^n)$, is also presented.