Expectation values and Fisher information theoretic measures of heavy flavoured mesons
The expectation values play important role in atomic physics and quantum mechanics. They are vital to obtaining the quantum information theoretic measures, Compton profile, electronic kinetic energy, Langevin-Pauli diamagnetic susceptibility, Dirac exchange energy and so on. In this work, however,...
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Nigerian Society of Physical Sciences
2025-02-01
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| Series: | Journal of Nigerian Society of Physical Sciences |
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| Online Access: | https://journal.nsps.org.ng/index.php/jnsps/article/view/2350 |
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| author | Ekwevugbe Omugbe ETIDO INYANG Arezu Jahanshir Clement A. Onate Cecilia N. Isonguyo Edwin S. Eyube Uduakobong S. Okorie Ridha Horchani Akpan N. Ikot |
| author_facet | Ekwevugbe Omugbe ETIDO INYANG Arezu Jahanshir Clement A. Onate Cecilia N. Isonguyo Edwin S. Eyube Uduakobong S. Okorie Ridha Horchani Akpan N. Ikot |
| author_sort | Ekwevugbe Omugbe |
| collection | DOAJ |
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The expectation values play important role in atomic physics and quantum mechanics. They are vital to obtaining the quantum information theoretic measures, Compton profile, electronic kinetic energy, Langevin-Pauli diamagnetic susceptibility, Dirac exchange energy and so on. In this work, however, we utilized the bound state solutions of the non-relativistic Schrödinger equation under the Cornell potential to obtain the expectation values using two analytical methods such as the integral approach and the Hellmann-Feynman theorem method. We applied the mean values to obtain the Fisher information theoretic measures for the Charmonium and Bottomonium mesons. We found that the mean values and probability densities are sensitive to the meson masses and the principal quantum number for fixed orbital quantum states. The Dirac exchange and the kinetic energies obey the lowest bound inequalities for 3D atomic systems. Also, the results obey the Fisher uncertainty product, Cramer-Rao and the Heisenberg uncertainty inequalities for 3D quantum systems.
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| format | Article |
| id | doaj-art-c19d7f572094400193a4c4b93b8cfc88 |
| institution | DOAJ |
| issn | 2714-2817 2714-4704 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | Journal of Nigerian Society of Physical Sciences |
| spelling | doaj-art-c19d7f572094400193a4c4b93b8cfc882025-08-20T02:46:44ZengNigerian Society of Physical SciencesJournal of Nigerian Society of Physical Sciences2714-28172714-47042025-02-017110.46481/jnsps.2025.2350Expectation values and Fisher information theoretic measures of heavy flavoured mesonsEkwevugbe Omugbe0ETIDO INYANG1Arezu Jahanshir2Clement A. Onate3Cecilia N. Isonguyo4Edwin S. Eyube5Uduakobong S. Okorie6Ridha Horchani7Akpan N. Ikot8Department of Physics, University of Agriculture and Environmental Sciences, Umuagwo, P.M.B. 1038, Imo State, NigeriaDepartment of Physics, National Open University of Nigeria, Abuja, NigeriaDepartment of Physics and Engineering Sciences, Buein Zahra Technical University, Buein Zahra, IranPhysics Department, Bowen University, Iwo, Osun State, NigeriaTheoretical Physics Group, Department of Physics, University of Uyo, Uyo, NigeriaDepartment of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, NigeriaDepartment of Physics, Akwa Ibom State University, Ikot Akpaden, Uyo, NigeriaDepartment of Physics, College of Science, Sultan Qaboos University, Muscat, Sultanate of OmanTheoretical Physics Group, Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria The expectation values play important role in atomic physics and quantum mechanics. They are vital to obtaining the quantum information theoretic measures, Compton profile, electronic kinetic energy, Langevin-Pauli diamagnetic susceptibility, Dirac exchange energy and so on. In this work, however, we utilized the bound state solutions of the non-relativistic Schrödinger equation under the Cornell potential to obtain the expectation values using two analytical methods such as the integral approach and the Hellmann-Feynman theorem method. We applied the mean values to obtain the Fisher information theoretic measures for the Charmonium and Bottomonium mesons. We found that the mean values and probability densities are sensitive to the meson masses and the principal quantum number for fixed orbital quantum states. The Dirac exchange and the kinetic energies obey the lowest bound inequalities for 3D atomic systems. Also, the results obey the Fisher uncertainty product, Cramer-Rao and the Heisenberg uncertainty inequalities for 3D quantum systems. https://journal.nsps.org.ng/index.php/jnsps/article/view/2350Mesons spectroscopyHellmann-Feynman theoremExpectation valuesFisher information |
| spellingShingle | Ekwevugbe Omugbe ETIDO INYANG Arezu Jahanshir Clement A. Onate Cecilia N. Isonguyo Edwin S. Eyube Uduakobong S. Okorie Ridha Horchani Akpan N. Ikot Expectation values and Fisher information theoretic measures of heavy flavoured mesons Journal of Nigerian Society of Physical Sciences Mesons spectroscopy Hellmann-Feynman theorem Expectation values Fisher information |
| title | Expectation values and Fisher information theoretic measures of heavy flavoured mesons |
| title_full | Expectation values and Fisher information theoretic measures of heavy flavoured mesons |
| title_fullStr | Expectation values and Fisher information theoretic measures of heavy flavoured mesons |
| title_full_unstemmed | Expectation values and Fisher information theoretic measures of heavy flavoured mesons |
| title_short | Expectation values and Fisher information theoretic measures of heavy flavoured mesons |
| title_sort | expectation values and fisher information theoretic measures of heavy flavoured mesons |
| topic | Mesons spectroscopy Hellmann-Feynman theorem Expectation values Fisher information |
| url | https://journal.nsps.org.ng/index.php/jnsps/article/view/2350 |
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