The aim of this work is to treat the time-independent one-dimensional nonlocal Schrodinger equation. The nonlocality is described by a kernel with a noninteger power α between 1 and 2. At first stage, by using Caputo–Fabrizio definition and other known results, we have transformed the nonlocal Schrodinger equation to an ordinary linear differential equation. Secondly, we have applied the last result to solve two problems in nonlocal quantum mechanics: the Coulomb-type and Hulthen-type potentials in one dimension. The eigenenergies and eigenfunctions are calculated. As expected, when the power α tends to two, the resulting solutions go to the standard case.

中文翻译：

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一些量子系统通过 Caputo-Fabrizio 定义的非局部薛定谔方程的解

这项工作的目的是处理与时间无关的一维非局部薛定谔方程。非局域性由具有 1 和 2 之间的非整数幂 α 的核描述。在第一阶段，通过使用 Caputo-Fabrizio 定义和其他已知结果，我们将非局域薛定谔方程转换为普通线性微分方程。其次，我们应用最后一个结果来解决非局域量子力学中的两个问题：一维的库仑型势和 Hulthen 型势。计算特征能量和特征函数。正如预期的那样，当幂 α 趋向于 2 时，结果解将进入标准情况。