A numerical formula is derived which gives solutions of the fractional Schrödinger equation in time-independent form in the case of Coulomb potential using Riemann–Liouville definition of the fractional derivative and the quadrature methods. The formula is applied for electron in the nucleus field for multiple values of fractional parameter of the space-dependent fractional Schrödinger equation and for each value of the space-dependent fractional parameter, multiple values of energies are applied. Distances are found at which the probability takes its maximum value. Values of energy obtained in this study corresponding to the maximum value of probability are compared with the energy values resulted from the fractional Bohr’s atom formula in the fractional quantum mechanics.

中文翻译：

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具有库仑势的时间无关分数阶薛定谔方程的迭代算法

在库仑势的情况下，使用分数阶导数的黎曼-刘维尔定义和求积方法，推导出了一个数值公式，该公式给出了时间无关形式的分数阶薛定谔方程的解。该公式适用于核场中电子的空间相关分数阶薛定谔方程的多个分数参数值，并且对于空间相关分数参数的每个值，应用多个能量值。找到概率取其最大值的距离。将本研究中对应于概率最大值的能量值与分数量子力学中分数玻尔原子公式得出的能量值进行比较。