In this paper the space-fractional Schrödinger equations with singular potentials are studied. Delta like or even higher-order singularities are allowed. By using the regularising techniques, we introduce a family of ‘weakened’ solutions, calling them very weak solutions. The existence, uniqueness and consistency results are proved in an appropriate sense. Numerical simulations are done, and a particles accumulating effect is observed in the singular cases. From the mathematical point of view a “splitting of the strong singularity” phenomena is also observed.

中文翻译：

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具有高阶奇异势的分数阶薛定ding方程

本文研究了具有奇异势能的空间分数维Schrödinger方程。允许类似Delta或什至更高阶的奇点。通过使用正则化技术，我们引入了一系列“弱化”的解决方案，称它们为非常弱的解决方案。证明了存在性，唯一性和一致性的结果是恰当的。进行了数值模拟，并在奇异情况下观察到了颗粒聚集效应。从数学观点来看，还观察到“强奇异性分裂”现象。