We revisit the derivation of the covariant two-body scalar-fermion equation with a Coulomb interaction, presented in a previous paper. We show that it can be given the formal aspect of a Dirac equation, but for the fact that the eigenvalue is also contained in one of the coefficients and thus it is not linearly included. The discussion of the boundary value problem is therefore different, although some properties of the Dirac equation can be recovered in an approximation bringing back to the concept of reduced mass. We discuss a mixed analytic-numerical method of solution which allows to obtain very accurate results and we calculate the lowest levels, states and QED corrections for pionic and kaonic atoms.

我们重新审视了具有库仑相互作用的协变二体标量-费米子方程的推导，在之前的一篇论文中提出。我们证明可以给出狄拉克方程的形式方面，但特征值也包含在系数之一中，因此它不是线性包含的。因此，对边值问题的讨论是不同的，尽管狄拉克方程的某些性质可以通过近似恢复到减少质量的概念。我们讨论了一种混合解析数值解法，它可以获得非常准确的结果，我们计算了 pionic 和 kaonic 原子的最低能级、状态和 QED 校正。