In this paper, we demonstrated that the multiple turning point problems within the framework of the Wentzel-Kramers-Brillouin (WKB) approximation method can be reduced to two turning point one for a nonsymmetric potential function by using an appropriate Pekeris-type approximation scheme. We solved the Schrödinger equation with the Killingbeck potential plus an inversely quadratic potential (KPIQP) function. The special cases of the modeled potential are discussed. We obtained the energy eigenvalues and the mass spectra of the heavy and heavy-light mesons systems. The results in this present work are in good agreement with the results obtained by other analytical methods and available experimental data in the literature.

中文翻译：

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通过WKB逼近法的介子质谱

在本文中，我们证明了通过使用适当的Pekeris型逼近方案，可以将Wentzel-Kramers-Brillouin（WKB）逼近方法框架内的多个转折点问题减少到两个转折点之一，以解决非对称势函数。我们用Killingbeck势加反二次势（KPIQP）函数求解了Schrödinger方程。讨论了建模潜力的特殊情况。我们获得了重介子和重介子系统的能量本征值和质谱。本工作中的结果与通过其他分析方法获得的结果和文献中的可用实验数据非常吻合。