Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm

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dc.authoridde la Sen, manuel/0000-0001-9320-9433
dc.contributor.authorLiaqat, Muhammad Imran
dc.contributor.authorAkgul, Ali
dc.contributor.authorDe la Sen, Manuel
dc.contributor.authorBayram, Mustafa
dc.date.accessioned2024-12-24T19:33:47Z
dc.date.available2024-12-24T19:33:47Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractThe entirety of the information regarding a subatomic particle is encoded in a wave function. Solving quantum mechanical models (QMMs) means finding the quantum mechanical wave function. Therefore, great attention has been paid to finding solutions for QMMs. In this study, a novel algorithm that combines the conformable Shehu transform and the Adomian decomposition method is presented that establishes approximate and exact solutions to QMMs in the sense of conformable derivatives with zero and nonzero trapping potentials. This solution algorithm is known as the conformable Shehu transform decomposition method (CSTDM). To evaluate the efficiency of this algorithm, the numerical results in terms of absolute and relative errors were compared with the reduced differential transform and the two-dimensional differential transform methods. The comparison showed excellent agreement with these methods, which means that the CSTDM is a suitable alternative tool to the methods based on the Caputo derivative for the solutions of time-fractional QMMs. The advantage of employing this approach is that, due to the use of the conformable Shehu transform, the pattern between the coefficients of the series solutions makes it simple to obtain the exact solution of both linear and nonlinear problems. Consequently, our approach is quick, accurate, and easy to implement. The convergence, uniqueness, and error analysis of the solution were examined using Banach's fixed point theory.
dc.description.sponsorshipBasque Government [IT1555-22, KK-2022/00090]; MCIN/AEI/FEDER, UE [PID2021-1235430B-C21, PID2021-1235430B-C22]
dc.description.sponsorshipThe authors are grateful to the Basque Government for its support throughGrants IT1555-22 and KK-2022/00090; and to (MCIN/AEI 269.10.13039/501100011033 /FEDER, UE)for Grants PID2021-1235430B-C21 and PID2021-1235430B-C22.
dc.identifier.doi10.3390/sym15030744
dc.identifier.issn2073-8994
dc.identifier.issue3
dc.identifier.scopus2-s2.0-85151627476
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/sym15030744
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8294
dc.identifier.volume15
dc.identifier.wosWOS:000959684200001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofSymmetry-Basel
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectconformable Shehu transform
dc.subjectquantum mechanics models
dc.subjectconformable derivative
dc.subjectAdomian decomposition method
dc.subjectapproximate solutions
dc.subjectexact solutions
dc.subjectsymmetry
dc.titleApproximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm
dc.typeArticle

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