广义不确定性原理方法中对库仑势的若干量子修正
On Some Quantum Correction to the Coulomb Potential in Generalized Uncertainty Principle Approach
AI总结：
本文基于广义不确定性原理研究修正薛定谔方程中的库仑势量子修正，提出Bethe ansatz方法求解该方程，并讨论结果及其与其他物理问题的类比。
摘要：
考虑到量子力学与引力统一理论的重要性，以及存在普朗克尺度量级的最小长度，我们研究了一个由广义不确定性原理导出的修正薛定谔方程。该方程在从量子信息领域到大尺度物理的范围内都有应用，并包含最近提出的经量子力学修正的引力相互作用。由于所得方程无法用常见的精确方法求解，我们提出一种Bethe ansatz方法，将其应用于该方程并讨论所得结果，同时评论本研究与其他一些有趣物理问题的类比。
英文摘要：
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.
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