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چکیده
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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 Schr¨odinger 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. Also, 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 calculated average kinetic and potential energies were found to possess an oscillatory motion occasioned by the quark-anti-quark interactions.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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