An upper bound for asymmetrical spinless Salpeter equations

TL;DR

This paper derives an analytical upper bound for the solutions of the spinless Salpeter equation with unequal masses using the auxiliary field method, focusing on Coulomb and linear potentials.

Contribution

It introduces a new analytical upper bound for the asymmetrical spinless Salpeter equation employing the auxiliary field method, applicable to specific potentials.

Findings

Derived an explicit upper bound for the equation with Coulomb potential.

Extended the bound to linear potential cases with a mass approaching zero.

Provided analytical expressions for the bounds in these scenarios.

Abstract

Using the auxiliary field method, a generic upper bound is obtained for the spinless Salpeter equation with two different masses. Analytical results are presented for the cases of the Coulomb and linear potentials when a mass is vanishing.