The Reduced Spinless Salpeter Wave Equation for Bound State Systems

In this work, the reduced spinless Salpeter equation is transformed into a relativistic second-order Schrödinger-like wave equation. The converted equation is so simple that one can solve it by using our proposed perturbation technique within the framework of the asymptotic iteration method. As an example, the Coulomb and Oscillator potential models are tested within this method. It is found that this method yields quite simple analytical solutions that will give rapidly the bound state energies with good accuracy compared with the available theoretical predictions. Furthermore, we predicted the relativistic energy eigenvalues of muonium, as well as, for the positronium bound states arising from the one-photon exchange in QED.