We propose Whittaker function approach as a theoretical method for finding exact solutions of a quantum mechanical system placed in the Kratzer potential. We then show that the effect of an external uniform magnetic field on this system can be satisfactorily determined using variational method. By following the one-step treatment suggested in this study, we increase the reliability and the accuracy of the solutions of Schrödinger equation for a quantum mechanical system placed in potential energy and perturbed by a uniform magnetic field that proves to be useful in modelling physical phenomena. We find that the achieved numerical and analytical results agree very well with those already published and those calculated using the Numerov method.

中文翻译：

---

置于 Kratzer 势和均匀磁场下的量子系统的精确解

我们提出 Whittaker 函数方法作为寻找位于 Kratzer 势中的量子力学系统的精确解的理论方法。然后我们表明可以使用变分方法令人满意地确定外部均匀磁场对该系统的影响。通过遵循本研究中建议的一步处理，我们提高了量子力学系统的薛定谔方程解的可靠性和准确性，该系统置于势能中并受到均匀磁场的干扰，这证明在模拟物理现象时很有用. 我们发现获得的数值和分析结果与那些已经发表的和使用 Numerov 方法计算的结果非常吻合。