论文标题
分数Schrödinger方程，具有高阶的单数电位
Fractional Schrödinger Equation with singular potentials of higher-order
论文作者
论文摘要
在本文中，研究了具有奇异电位的空间散文schrödinger方程。允许类似三角洲的奇异性。通过使用正规化技术，我们介绍了一个“削弱”解决方案的家庭，称它们非常薄弱。在适当的意义上证明了存在，独特性和一致性结果。进行数值模拟，并在单数情况下观察到粒子的积累效果。从数学的角度来看，还观察到“强奇异性的分裂”现象。
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 particle accumulating effect is observed in the singular cases. From the mathematical point of view, a "splitting of the strong singularity" phenomena is also observed.
