Fractional Schrödinger equation with singular potentials of higher order
- Author
- Arshyn Altybay, Michael Ruzhansky (UGent) , Mohammed Elamine Sebih and Niyaz Tokmagambetov (UGent)
- Organization
- Project
- Abstract
- 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.
- Keywords
- Mathematical Physics, Statistical and Nonlinear Physics, Schrodinger equation, fractional Laplacian, generalised solution, singular potential, regularisation, numerical analysis, distributional coefficient, very weak solution
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8757012
- MLA
- Altybay, Arshyn, et al. “Fractional Schrödinger Equation with Singular Potentials of Higher Order.” REPORTS ON MATHEMATICAL PHYSICS, vol. 87, no. 1, 2021, pp. 129–44, doi:10.1016/s0034-4877(21)00016-1.
- APA
- Altybay, A., Ruzhansky, M., Sebih, M. E., & Tokmagambetov, N. (2021). Fractional Schrödinger equation with singular potentials of higher order. REPORTS ON MATHEMATICAL PHYSICS, 87(1), 129–144. https://doi.org/10.1016/s0034-4877(21)00016-1
- Chicago author-date
- Altybay, Arshyn, Michael Ruzhansky, Mohammed Elamine Sebih, and Niyaz Tokmagambetov. 2021. “Fractional Schrödinger Equation with Singular Potentials of Higher Order.” REPORTS ON MATHEMATICAL PHYSICS 87 (1): 129–44. https://doi.org/10.1016/s0034-4877(21)00016-1.
- Chicago author-date (all authors)
- Altybay, Arshyn, Michael Ruzhansky, Mohammed Elamine Sebih, and Niyaz Tokmagambetov. 2021. “Fractional Schrödinger Equation with Singular Potentials of Higher Order.” REPORTS ON MATHEMATICAL PHYSICS 87 (1): 129–144. doi:10.1016/s0034-4877(21)00016-1.
- Vancouver
- 1.Altybay A, Ruzhansky M, Sebih ME, Tokmagambetov N. Fractional Schrödinger equation with singular potentials of higher order. REPORTS ON MATHEMATICAL PHYSICS. 2021;87(1):129–44.
- IEEE
- [1]A. Altybay, M. Ruzhansky, M. E. Sebih, and N. Tokmagambetov, “Fractional Schrödinger equation with singular potentials of higher order,” REPORTS ON MATHEMATICAL PHYSICS, vol. 87, no. 1, pp. 129–144, 2021.
@article{8757012,
abstract = {{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.}},
author = {{Altybay, Arshyn and Ruzhansky, Michael and Sebih, Mohammed Elamine and Tokmagambetov, Niyaz}},
issn = {{0034-4877}},
journal = {{REPORTS ON MATHEMATICAL PHYSICS}},
keywords = {{Mathematical Physics,Statistical and Nonlinear Physics,Schrodinger equation,fractional Laplacian,generalised solution,singular potential,regularisation,numerical analysis,distributional coefficient,very weak solution}},
language = {{eng}},
number = {{1}},
pages = {{129--144}},
title = {{Fractional Schrödinger equation with singular potentials of higher order}},
url = {{http://doi.org/10.1016/s0034-4877(21)00016-1}},
volume = {{87}},
year = {{2021}},
}
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