A Fractional Schrodinger Equation and Its Solution
| dc.contributor.author | Agrawal, Om P. | |
| dc.contributor.author | Baleanu, Dumitru | |
| dc.contributor.author | Muslih, Sami I. | |
| dc.date.accessioned | 2016-06-09T08:05:45Z | |
| dc.date.accessioned | 2025-09-18T14:09:58Z | |
| dc.date.available | 2016-06-09T08:05:45Z | |
| dc.date.available | 2025-09-18T14:09:58Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | This paper presents a fractional Schrodinger equation and its solution. The fractional Schrodinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrodinger equation of order alpha. We also use a fractional Klein-Gordon equation to obtain the fractional Schrodinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function. | en_US |
| dc.description.sponsorship | Institute of International Education, New York, NY; Department of Mechanical Engineering and Energy Processes (MEEP); Southern Illinois University, Carbondale (SIUC), IL; Al-Azhar University-Gaza; Scientific and Technical Research Council of Turkey | en_US |
| dc.description.sponsorship | One of the authors (S.M.) would like to sincerely thank the Institute of International Education, New York, NY, and the Department of Mechanical Engineering and Energy Processes (MEEP) and the Dean of Graduate Studies at Southern Illinois University, Carbondale (SIUC), IL, for providing him the financial support and the necessary facilities during his stay at SIUC. Also he would like to thank the Deanship of Graduate studies at Al-Azhar University-Gaza for support. This work is partially supported by the Scientific and Technical Research Council of Turkey. | en_US |
| dc.identifier.citation | Muslih, S.I., Baleanu, D., Agrawal, O.P. (2010). A fractional schrödinger equation and its solution. International Journal of Theoretical Physics, 49(8), 1746-1752. http://dx.doi.org/ 10.1007/s10773-010-0354-x | en_US |
| dc.identifier.doi | 10.1007/s10773-010-0354-x | |
| dc.identifier.issn | 0020-7748 | |
| dc.identifier.issn | 1572-9575 | |
| dc.identifier.scopus | 2-s2.0-77955274090 | |
| dc.identifier.uri | https://doi.org/10.1007/s10773-010-0354-x | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12416/13546 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer/plenum Publishers | en_US |
| dc.relation.ispartof | International Journal of Theoretical Physics | |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Lagrangian And Hamiltonian Approach | en_US |
| dc.title | A Fractional Schrodinger Equation and Its Solution | en_US |
| dc.title | A fractional schrödinger equation and its solution | tr_TR |
| dc.type | Article | en_US |
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| gdc.author.wosid | Baleanu, Dumitru/B-9936-2012 | |
| gdc.author.wosid | Muslih, Sami/Aaf-4974-2020 | |
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| gdc.description.department | Çankaya University | en_US |
| gdc.description.departmenttemp | [Baleanu, Dumitru] Cankaya Univ, Fac Arts & Sci, Dept Math & Comp Sci, TR-06530 Ankara, Turkey; [Muslih, Sami I.; Agrawal, Om P.] So Illinois Univ, Dept Mech Engn, Carbondale, IL 62901 USA | en_US |
| gdc.description.endpage | 1752 | en_US |
| gdc.description.issue | 8 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
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| gdc.description.startpage | 1746 | en_US |
| gdc.description.volume | 49 | en_US |
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| gdc.oaire.keywords | Fractional derivatives and integrals | |
| gdc.oaire.keywords | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics | |
| gdc.oaire.keywords | Variational principles of physics | |
| gdc.oaire.keywords | Lagrangian and Hamiltonian approach | |
| gdc.oaire.keywords | Fractional partial differential equations | |
| gdc.oaire.keywords | Lagrange's equations | |
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