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arXiv · 2004.10182

Fractional Schr\"{o}dinger Equation with singular potentials of higher-order

Arshyn Altybay·Michael Ruzhansky·Mohammed Elamine Sebih·Niyaz Tokmagambetov
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Abstract

In this paper, the space-fractional Schr\"{o}dinger 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.

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Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov. 2020-04-21. Fractional Schr\"{o}dinger Equation with singular potentials of higher-order. https://arxiv.org/abs/2004.10182

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