Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials
Abstract The bound-state solution of the radial Klein-Gordon equation has been obtained under the interaction of an exponential-type and Yukawa potential functions. The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy an...
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Nature Portfolio
2024-11-01
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| Online Access: | https://doi.org/10.1038/s41598-024-80123-9 |
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| author | R. Horchani E. Omugbe I. J. Njoku L. M. Pérez C. A. Onate A. Jahanshir E. Feddi K. O. Emeje E. S. Eyube |
| author_facet | R. Horchani E. Omugbe I. J. Njoku L. M. Pérez C. A. Onate A. Jahanshir E. Feddi K. O. Emeje E. S. Eyube |
| author_sort | R. Horchani |
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| description | Abstract The bound-state solution of the radial Klein-Gordon equation has been obtained under the interaction of an exponential-type and Yukawa potential functions. The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy and wave functions in closed form. The momentum space wave function in D dimensions has been constructed using the Fourier transform. The mean values have been conjectured for the position and momentum spaces using two equivalent equations. The effects of the potential parameters on the expectation values and quantum information measurement have been investigated. For the 1D case, the results obey the Heisenberg uncertainty principle, Fisher, Shannon, Onicescu, and the Rényi entropic inequalities. Other information complexities measures, such as Shannon Power, Fisher-Shannon, and Lopez-Ruiz-Mancini-Calbet, have been verified. For the ground state, the 1D momentum expectation value $$\langle p^{2} \rangle_{00}$$ coincides with the 3D $$\langle p^{2} \rangle_{000}$$ values, which is an indication of degeneracy. The total energy of a particle in both 1D and 3D space may be degenerate due to the inter-dimensional degeneracy of the quantum numbers. However, in this present result, the degeneracy in 1D and 3D occurred for fixed quantum states at different momentum intervals. Thus, in 1D, a particle may transit an entire space ( $$\:-\infty\:<p<\infty\:)$$ with a certain kinetic energy, which must be equal to its kinetic energy if it moves through the interval $$\:0<p<\infty\:$$ in 3D space. This may have implications for kinetic energy degeneracy in higher dimensions. |
| format | Article |
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| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-7b5c6e04e98b4b9b85260471e6b71d1e2024-11-24T12:22:47ZengNature PortfolioScientific Reports2045-23222024-11-0114112110.1038/s41598-024-80123-9Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentialsR. Horchani0E. Omugbe1I. J. Njoku2L. M. Pérez3C. A. Onate4A. Jahanshir5E. Feddi6K. O. Emeje7E. S. Eyube8Department of Physics, College of Science, Sultan Qaboos UniversityDepartment of Physics, University of Agriculture and Environmental SciencesDepartment of Physics, Federal University of Technology OwerriDepartmento de Física, Universidad de TarapacáDepartment of Physics, Bowen UniversityDepartment of Physics and Engineering Sciences, Buein Zahra, Technical UniversityGroup of Optoelectronic of semiconductors and Nanomaterials, ENSAM, Mohammed V UniversityDepartment of Physics, Kogi State UniversityDepartment of Physics, Faculty of Physical Sciences, Modibbo Adama UniversityAbstract The bound-state solution of the radial Klein-Gordon equation has been obtained under the interaction of an exponential-type and Yukawa potential functions. The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy and wave functions in closed form. The momentum space wave function in D dimensions has been constructed using the Fourier transform. The mean values have been conjectured for the position and momentum spaces using two equivalent equations. The effects of the potential parameters on the expectation values and quantum information measurement have been investigated. For the 1D case, the results obey the Heisenberg uncertainty principle, Fisher, Shannon, Onicescu, and the Rényi entropic inequalities. Other information complexities measures, such as Shannon Power, Fisher-Shannon, and Lopez-Ruiz-Mancini-Calbet, have been verified. For the ground state, the 1D momentum expectation value $$\langle p^{2} \rangle_{00}$$ coincides with the 3D $$\langle p^{2} \rangle_{000}$$ values, which is an indication of degeneracy. The total energy of a particle in both 1D and 3D space may be degenerate due to the inter-dimensional degeneracy of the quantum numbers. However, in this present result, the degeneracy in 1D and 3D occurred for fixed quantum states at different momentum intervals. Thus, in 1D, a particle may transit an entire space ( $$\:-\infty\:<p<\infty\:)$$ with a certain kinetic energy, which must be equal to its kinetic energy if it moves through the interval $$\:0<p<\infty\:$$ in 3D space. This may have implications for kinetic energy degeneracy in higher dimensions.https://doi.org/10.1038/s41598-024-80123-9Radial Klein-Gordon equationShannon EntropyRenyi entropyFisher informationKinetic energy |
| spellingShingle | R. Horchani E. Omugbe I. J. Njoku L. M. Pérez C. A. Onate A. Jahanshir E. Feddi K. O. Emeje E. S. Eyube Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials Scientific Reports Radial Klein-Gordon equation Shannon Entropy Renyi entropy Fisher information Kinetic energy |
| title | Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials |
| title_full | Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials |
| title_fullStr | Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials |
| title_full_unstemmed | Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials |
| title_short | Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials |
| title_sort | relativistic bound state solutions and quantum information theory in d dimensions under exponential type plus yukawa potentials |
| topic | Radial Klein-Gordon equation Shannon Entropy Renyi entropy Fisher information Kinetic energy |
| url | https://doi.org/10.1038/s41598-024-80123-9 |
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