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.

在这项工作中，将简化的无旋转Salpeter方程转换为相对论性的类似于Schrödinger的二阶波动方程。转换后的方程是如此简单，以至于人们可以在渐进迭代​​方法的框架内使用我们提出的摄动技术来求解它。例如，在此方法中测试了库仑和振荡器势模型。发现该方法产生了非常简单的分析解决方案，与可用的理论预测相比，该解决方案将以良好的精度快速给出束缚态能量。此外，我们预测了Q的相对论能量本征值，以及由于QED中的单光子交换引起的正电子束缚态。