标题： 相对论单粒子态的计算 显示英文标题

标题： Calculation of Relativistic Single-Particle States

摘要： 提出了一种计算束缚态和共振态的计算方法，分别通过求解实能和复能情况下的克莱因-戈登方程和狄拉克方程。 该方法是对非相对论方法的扩展，在该方法中，势能用库仑-斯特姆函数基来表示。 该基有助于以连分数形式对库仑格林算符进行精确的解析评估。 在扩展到相对论问题时，我们将克莱因-戈登方程和狄拉克方程转化为有效的薛定谔形式。 然后，求解方法基本上是将诸如角动量、电荷、能量和势能等非相对论量解析延拓为有效的相对论对应量。 显示英文摘要

摘要： A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential is represented in a Coulomb-Sturmian basis. This basis facilitates the exact analytic evaluation of the Coulomb Green's operator in terms of a continued fraction. In the extension to relativistic problems, we cast the Klein-Gordon and Dirac equations into an effective Schr\"odinger form. Then the solution method is basically an analytic continuation of non-relativistic quantities like the angular momentum, charge, energy and potential into the effective relativistic counterparts.