In this paper, the Dirac equation in the presence of some scalar potentials based on sl (2) Lie algebra is solved by quasi-exact solvability theory. The configuration of the classes III and VI potentials in the Turbiner’s classification is constructed. Then, the Bethe ansatz equations are calculated so that the energy eigenvalues and eigenfunctions are obtained. Also, we study the problem by using asymptotic iteration method. Finally, we compare the results obtained by these two methods.

中文翻译：

---

存在一些标量势时狄拉克方程的拟精确和渐近迭代解

本文利用拟精确可解性理论求解了基于sl(2)李代数的一些标量势存在下的狄拉克方程。构建了涡轮机分类中的 III 类和 VI 类电位的配置。然后，计算 Bethe ansatz 方程，从而获得能量特征值和特征函数。此外，我们使用渐近迭代方法研究该问题。最后，我们比较了这两种方法得到的结果。