Expectation values and Fisher information theoretic measures of heavy flavoured mesons

Ekwevugbe Omugbe; ETIDO INYANG; Arezu Jahanshir; Clement A. Onate; Cecilia N. Isonguyo; Edwin S. Eyube; Uduakobong S. Okorie; Ridha Horchani; Akpan N. Ikot

doi:10.46481/jnsps.2025.2350

Authors

E. Omugbe
[email protected]

Department of Physics, University of Agriculture and Environmental Sciences, Umuagwo, P.M.B. 1038, Imo State, Nigeria
E. P. Inyang
Department of Physics, National Open University of Nigeria, Abuja, Nigeria
A. Jahanshir
Department of Physics and Engineering Sciences, Buein Zahra Technical University, Buein Zahra, Iran
C. A. Onate
Physics Department, Bowen University, Iwo, Osun State, Nigeria
C. N. Isonguyo
Theoretical Physics Group, Department of Physics, University of Uyo, Uyo, Nigeria
E. S. Eyube
Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
U. S. Okorie
Department of Physics, Akwa Ibom State University, Ikot Akpaden, Uyo, Nigeria
R. Horchani
Department of Physics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman
A. N. Ikot
Theoretical Physics Group, Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria

Keywords:

Mesons spectroscopy, Hellmann-Feynman theorem, Expectation values, Fisher information

Abstract

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.

Dimensions

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