Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm
The 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 com...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/3/744 |
| _version_ | 1797608867726622720 |
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| author | Muhammad Imran Liaqat Ali Akgül Manuel De la Sen Mustafa Bayram |
| author_facet | Muhammad Imran Liaqat Ali Akgül Manuel De la Sen Mustafa Bayram |
| author_sort | Muhammad Imran Liaqat |
| collection | DOAJ |
| description | The 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. |
| first_indexed | 2024-03-11T05:50:32Z |
| format | Article |
| id | doaj.art-b86c9d73b9cd49b6ae61b3d8dfa718ce |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T05:50:32Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b86c9d73b9cd49b6ae61b3d8dfa718ce2023-11-17T14:10:22ZengMDPI AGSymmetry2073-89942023-03-0115374410.3390/sym15030744Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel AlgorithmMuhammad Imran Liaqat0Ali Akgül1Manuel De la Sen2Mustafa Bayram3Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New MuslimTown, Lahore 54600, PakistanDepartment of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, LebanonDepartment of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, SpainDepartment of Computer Engineering, Biruni University, Istanbul 34010, TurkeyThe 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.https://www.mdpi.com/2073-8994/15/3/744conformable Shehu transformquantum mechanics modelsconformable derivativeAdomian decomposition methodapproximate solutionsexact solutions |
| spellingShingle | Muhammad Imran Liaqat Ali Akgül Manuel De la Sen Mustafa Bayram Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm Symmetry conformable Shehu transform quantum mechanics models conformable derivative Adomian decomposition method approximate solutions exact solutions |
| title | Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm |
| title_full | Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm |
| title_fullStr | Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm |
| title_full_unstemmed | Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm |
| title_short | Approximate and Exact Solutions in the Sense of Conformable Derivatives of Quantum Mechanics Models Using a Novel Algorithm |
| title_sort | approximate and exact solutions in the sense of conformable derivatives of quantum mechanics models using a novel algorithm |
| topic | conformable Shehu transform quantum mechanics models conformable derivative Adomian decomposition method approximate solutions exact solutions |
| url | https://www.mdpi.com/2073-8994/15/3/744 |
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