Fractional Schrödinger Equation with Singular Potentials of Higher Order

Autor:	Arshyn Altybay, Mohammed Elamine Sebih, Niyaz Tokmagambetov, Michael Ruzhansky
Rok vydání:	2021
Předmět:	Order (ring theory) Statistical and Nonlinear Physics Delta like 1 Schrödinger equation symbols.namesake Singularity Consistency (statistics) symbols Point (geometry) Gravitational singularity Uniqueness Mathematical Physics Mathematics Mathematical physics
Zdroj:	Reports on Mathematical Physics. 87:129-144
ISSN:	0034-4877
DOI:	10.1016/s0034-4877(21)00016-1
Popis:	In this paper the space-fractional Schrodinger 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::840d68ebe1e633398556ed596b21ac80 https://doi.org/10.1016/s0034-4877(21)00016-1 Zobrazit plný text záznamu Full Text from ScienceDirect