Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation
In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density p...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/5178247 |
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| author | Ituen Okon Clement Onate Ekwevugbe Omugbe Uduakobong Okorie Akaninyene Antia Michael Onyeaju Chen Wen-Li Judith Araujo |
| author_facet | Ituen Okon Clement Onate Ekwevugbe Omugbe Uduakobong Okorie Akaninyene Antia Michael Onyeaju Chen Wen-Li Judith Araujo |
| author_sort | Ituen Okon |
| collection | DOAJ |
| description | In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential). The proposed potential is best suitable for smaller values of the screening parameter α. The resulting energy eigenvalue is presented in a close form and extended to study thermal properties and superstatistics expressed in terms of partition function Z and other thermodynamic properties such as vibrational mean energy U, vibrational specific heat capacity C, vibrational entropy S, and vibrational free energy F. Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtained for various values of the screening parameter (α) as well as different expectation values via Hellmann-Feynman Theorem (HFT). The trend of the partition function and other thermodynamic properties obtained for both thermal properties and superstatistics were in excellent agreement with the existing literatures. Due to the analytical mathematical complexities, the superstatistics and thermal properties were evaluated using Mathematica 10.0 version software. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential, and Coulomb potential as special cases. |
| format | Article |
| id | doaj-art-c4c2747f7db940efb8c060a5f5bfe5e3 |
| institution | Kabale University |
| issn | 1687-7365 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-c4c2747f7db940efb8c060a5f5bfe5e32025-02-03T05:59:04ZengWileyAdvances in High Energy Physics1687-73652022-01-01202210.1155/2022/5178247Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger EquationItuen Okon0Clement Onate1Ekwevugbe Omugbe2Uduakobong Okorie3Akaninyene Antia4Michael Onyeaju5Chen Wen-Li6Judith Araujo7University of UyoLandmark UniversityFederal University of Petroleum ResourcesAkwa Ibom State UniversityUniversity of UyoUniversity of Port HarcourtXi’an Peihua UniversityInstituto Federal do Sudeste de Minas GeraisIn this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential). The proposed potential is best suitable for smaller values of the screening parameter α. The resulting energy eigenvalue is presented in a close form and extended to study thermal properties and superstatistics expressed in terms of partition function Z and other thermodynamic properties such as vibrational mean energy U, vibrational specific heat capacity C, vibrational entropy S, and vibrational free energy F. Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtained for various values of the screening parameter (α) as well as different expectation values via Hellmann-Feynman Theorem (HFT). The trend of the partition function and other thermodynamic properties obtained for both thermal properties and superstatistics were in excellent agreement with the existing literatures. Due to the analytical mathematical complexities, the superstatistics and thermal properties were evaluated using Mathematica 10.0 version software. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential, and Coulomb potential as special cases.http://dx.doi.org/10.1155/2022/5178247 |
| spellingShingle | Ituen Okon Clement Onate Ekwevugbe Omugbe Uduakobong Okorie Akaninyene Antia Michael Onyeaju Chen Wen-Li Judith Araujo Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation Advances in High Energy Physics |
| title | Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation |
| title_full | Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation |
| title_fullStr | Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation |
| title_full_unstemmed | Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation |
| title_short | Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation |
| title_sort | approximate solutions thermal properties and superstatistics solutions to schrodinger equation |
| url | http://dx.doi.org/10.1155/2022/5178247 |
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