Spectral structure and solution of fractional hydrogen atom difference equations
In this study, discrete fractional hydrogen atom (DFHA) operators are presented. Hydrogen atom differential equations have series solution due to having singularity and also obtaining a series solution for DFHA equations have some difficulties, for this reason, we study to obtain solution of DFHA eq...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020093/fulltext.html |
| _version_ | 1818508703236620288 |
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| author | Erdal Bas Ramazan Ozarslan Resat Yilmazer |
| author_facet | Erdal Bas Ramazan Ozarslan Resat Yilmazer |
| author_sort | Erdal Bas |
| collection | DOAJ |
| description | In this study, discrete fractional hydrogen atom (DFHA) operators are presented. Hydrogen atom differential equations have series solution due to having singularity and also obtaining a series solution for DFHA equations have some difficulties, for this reason, we study to obtain solution of DFHA equations by means of nabla Laplace transform. In addition to all these, we show self-adjointness of the DFHA operator and some spectral properties, like orthogonality of distinct eigenfunctions, reality of eigenvalues. Finally, we find an analytical solution of the problem under different <em>q</em> (<em>t</em>) potential functions, different fractional orders and different eigenvalues and the results obtained are illustrated by tables and simulations. |
| first_indexed | 2024-12-10T22:35:39Z |
| format | Article |
| id | doaj.art-d42d5e1bc5c44ac68271370ed7fcbcff |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T22:35:39Z |
| publishDate | 2020-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-d42d5e1bc5c44ac68271370ed7fcbcff2022-12-22T01:30:54ZengAIMS PressAIMS Mathematics2473-69882020-01-01521359137110.3934/math.2020093Spectral structure and solution of fractional hydrogen atom difference equationsErdal Bas0Ramazan Ozarslan1Resat Yilmazer2Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, TurkeyDepartment of Mathematics, Science Faculty, Firat University, 23119 Elazig, TurkeyDepartment of Mathematics, Science Faculty, Firat University, 23119 Elazig, TurkeyIn this study, discrete fractional hydrogen atom (DFHA) operators are presented. Hydrogen atom differential equations have series solution due to having singularity and also obtaining a series solution for DFHA equations have some difficulties, for this reason, we study to obtain solution of DFHA equations by means of nabla Laplace transform. In addition to all these, we show self-adjointness of the DFHA operator and some spectral properties, like orthogonality of distinct eigenfunctions, reality of eigenvalues. Finally, we find an analytical solution of the problem under different <em>q</em> (<em>t</em>) potential functions, different fractional orders and different eigenvalues and the results obtained are illustrated by tables and simulations.https://www.aimspress.com/article/10.3934/math.2020093/fulltext.htmlhydrogen atomdiscrete fractionalelectroneigenvalueschrödinger equationenergy level |
| spellingShingle | Erdal Bas Ramazan Ozarslan Resat Yilmazer Spectral structure and solution of fractional hydrogen atom difference equations AIMS Mathematics hydrogen atom discrete fractional electron eigenvalue schrödinger equation energy level |
| title | Spectral structure and solution of fractional hydrogen atom difference equations |
| title_full | Spectral structure and solution of fractional hydrogen atom difference equations |
| title_fullStr | Spectral structure and solution of fractional hydrogen atom difference equations |
| title_full_unstemmed | Spectral structure and solution of fractional hydrogen atom difference equations |
| title_short | Spectral structure and solution of fractional hydrogen atom difference equations |
| title_sort | spectral structure and solution of fractional hydrogen atom difference equations |
| topic | hydrogen atom discrete fractional electron eigenvalue schrödinger equation energy level |
| url | https://www.aimspress.com/article/10.3934/math.2020093/fulltext.html |
| work_keys_str_mv | AT erdalbas spectralstructureandsolutionoffractionalhydrogenatomdifferenceequations AT ramazanozarslan spectralstructureandsolutionoffractionalhydrogenatomdifferenceequations AT resatyilmazer spectralstructureandsolutionoffractionalhydrogenatomdifferenceequations |