Lower bounds for the spinless Salpeter equation

TL;DR

This paper derives lower bounds for the ground state energy of the spinless Salpeter equation in one and three dimensions, applicable to certain classes of potentials, including some confining ones.

Contribution

It provides new lower bounds for the relativistic Schrödinger equation's ground state energy, extending to confining potentials not in standard integrability classes.

Findings

Lower bounds established for potentials in $L^p( ^n)$ with $p>n$

Extension of bounds to confining potentials outside $L^p$ classes

Applicable in both one and three dimensions

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.