We apply the supersymmetric quantum mechanics and shape invariance approach to obtain the solutions of the 3-dimensional Schrödinger equation in the presence of a newly proposed potential model called hyperbolic-sinus potential function for any ℓ−state. Rotational-vibrational energy eigenvalues of some diatomic molecules are numerically calculated. Special cases of interest of the hyperbolic-sinus potential function are also studied. Our results indicated that the energy eigenvalue is highly sensitive to the potential parameters.

中文翻译：

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薛定ding方程的束缚态解及其在某些双原子分子上的应用。

我们采用超对称量子力学和形状不变的方法来获得所要求的任何双曲窦潜在功能的新提出的势模型存在的3维薛定谔方程的解ℓ -状态。数值计算了一些双原子分子的旋转振动能量本征值。还研究了双曲线窦势函数感兴趣的特殊情况。我们的结果表明，能量特征值对潜在参数高度敏感。