In this study, the radial Schrödinger equation is solved with the screened Kratzer potential using the series expansion method. The bound state energy spectra are obtained. To check the correctness of the result obtained from this method, we carry out suitable adjustments to the screened Kratzer potential parameters resulting in potential models, such as the Kratzer and Coulomb potentials are deduced as special cases. The numerical values of the energy spectra of the special cases (Kratzer potential) for hydrogen chloride and lithium hydride diatomic molecules are computed for different quantum numbers; n and l and the results are in consonance with the theoretical works of similar investigation. The expression for the energy spectra is applied to obtain the mass spectra of heavy quarkonium systems (charmonium and bottomonium). The numerical results agree with the experimental values and theoretical studies in previous works. Our results will have possible applications in high energy physics, molecular physics, etc.

在这项研究中，使用级数展开法用屏蔽的Kratzer势求解径向Schrödinger方程。获得了束缚态能谱。为了检查从该方法获得的结果的正确性，我们对筛选出的Kratzer电势参数进行了适当的调整，从而得出了电势模型，例如在特殊情况下推导了Kratzer电势和库仑电势。计算了不同量子数下氯化氢和氢化锂双原子分子特殊情况下的能谱数值（Kratzer势）。n和l结果与类似研究的理论工作相吻合。应用能谱的表达式来获得重的夸克铵体系（铵和systems）的质谱。数值结果与以往的实验值和理论研究相吻合。我们的结果将在高能物理，分子物理等领域具有可能的应用。