The generalized Woods–Saxon potential plus repulsive Coulomb interaction is considered in this work. The supersymmetry quantum mechanics method is used to get the energy spectrum of Schrodinger equation and also the Nikiforov–Uvarov approach is employed to solve analytically the Schrodinger equation in the framework of quantum mechanics. The potentials with centrifugal term include both exponential and radial terms, hence, the Pekeris approximation is considered to approximate the radial terms. By using the step-by-step Nikiforov–Uvarov method, the energy eigenvalue and wave function are obtained analytically. After that, the spectrum of energy is obtained by the supersymmetry quantum mechanics method. The energy eigenvalues obtained from each method are the same. Then in special cases, the results are compared with former result and a full agreement is observed. In the S-state, the standard Woods–Saxon potential has no bound state, but with Coulomb repulsive interaction, it may have bound state for zero angular momentum.

中文翻译：

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通过 Nikiforov-Uvarov 和超对称量子力学方法对 Woods-Saxon 势加库仑相互作用的薛定谔方程的束缚态解

在这项工作中考虑了广义的伍兹-撒克逊势加上排斥的库仑相互作用。采用超对称量子力学方法得到薛定谔方程的能谱，并采用Nikiforov-Uvarov方法在量子力学框架下解析求解薛定谔方程。具有离心项的势包括指数项和径向项，因此，Pekeris 近似被认为是近似径向项。采用分步 Nikiforov-Uvarov 方法，解析得到能量特征值和波函数。之后，通过超对称量子力学方法获得能量谱。每种方法得到的能量特征值是相同的。那么在特殊情况下，将结果与以前的结果进行比较，观察到完全一致。在里面小号态，标准的伍兹-撒克逊势没有束缚态，但在库仑排斥作用下，它可能具有零角动量的束缚态。