Taking into account the importance of the unified theory of quantum mechanics and gravity, and the existence of a minimal length of the order of the Planck scale, we consider a modified Schrödinger equation resulting from a generalized uncertainty principle, which finds applications from the realm of quantum information to large-scale physics, with a quantum mechanically corrected gravitational interaction proposed very recently. As the resulting equation cannot be solved by common exact approaches, we propose a Bethe ansatz approach, which will be applied and whose results we will discuss, commenting on the analogy of the present study with some other interesting physical problems.

中文翻译：

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关于广义不确定性原理方法中库仑势的量子修正

考虑到量子力学和引力统一理论的重要性，以及普朗克尺度阶次最小长度的存在，我们考虑由广义不确定性原理得出的修正薛定谔方程，该方程在以下领域找到了应用：最近提出了量子力学校正的引力相互作用，将量子信息应用于大规模物理。由于所得方程无法通过常见的精确方法求解，因此我们提出了 Bethe ansatz 方法，我们将应用该方法并讨论其结果，并对本研究与其他一些有趣的物理问题的类比进行评论。