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 (Schrödinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts are in $L^p({\mathbb{R}}^n)$ for some $p>n$ ($n=1$ or 3). An extension to confining potentials, which are not in $L^p({\mathbb{R}}^n)$, is also presented.

11 pages, 2 figures. Contribution to a special issue of Journal of Nonlinear Mathematical Physics in honour of Francesco Calogero on the occasion of his seventieth birthday

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