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arXiv:2301.11627 · Results in Physics

Quantum information entropy of heavy mesons in the presence of a point-like defect

C. A. S. Almeida, Collins Okon Edet, F. C. E. Lima, Norshamsuri Ali, Muhammad Asjad

Published Mar 6, 2023• 5 citations
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Abstract

Using Schrödinger’s formalism, we investigate the quantum eigenstates of the heavy mesons trapped by a point-like defect and by Cornell’s potential. One implements this defect to the model considering a spherical metric profile coupled to it. Furthermore, the Nikiforov–Uvarov method is applied to theory to study the quantum eigenstates of the heavy mesons. To calculate the quantum information entropy (QIE), one considers the wave functions that describe the charmonium and bottomonium states. To explore the QIE, we use the well-known Shannon’s entropy formulated at the position and reciprocal space. The analysis of the QIE gives us relevant information about how the quantum information change with the variation of the point-like defect. Consequently, considering the Bialynicki-Birula and Mycielski (BBM) relation, we show how this defect influences the quarkonium position and momentum uncertainty measures.

DOI
10.1016/j.rinp.2023.106343

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Using Schrödinger’s formalism, we investigate the quantum eigenstates of the heavy mesons trapped by a point-like defect and by Cornell’s potential. One implements this defect to the model considering a spherical metric profile coupled to it. Furthermore, the Nikiforov–Uvarov method is applied to theory to study the quantum eigenstates of the heavy mesons. To calculate the quantum information entropy (QIE), one considers the wave functions that describe the charmonium and bottomonium states. To explore the QIE, we use the well-known Shannon’s entropy formulated at the position and reciprocal space. The analysis of the QIE gives us relevant information about how the quantum information change with the variation of the point-like defect. Consequently, considering the Bialynicki-Birula and Mycielski (BBM) relation, we show how this defect influences the quarkonium position and momentum uncertainty measures.
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Shannon entropy for lower position and momentum eigenstates of Pöschl—Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density ρ( x ) moves right when the potential parameter V 1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter | V 2 |. Concerning the momentum information entropy density ρ( p ), we observe that its amplitude increases with increasing potential parameter V 1 , but its amplitude decreases with increasing | V 2 |. The Bialynicki—Birula—Mycielski (BBM) inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V 1 , but decreases with | V 2 |. However, the variation of momentum information entropy is contrary to that of the position information entropy.
In this study, the energy equation and normalized wave function were obtained by solving the Schrödinger equation analytically utilizing the Eckart-Hellmann potential and the Nikiforov-Uvarov method. Fisher information and Shannon entropy were investigated. Our results showed higher-order characteristic behavior for position and momentum space. Our numerical results showed an increase in the accuracy of the location of the predicted particles occurring in the position space. Also, our results show that the sum of the position and momentum entropies satisfies the lower-bound Berkner, Bialynicki-Birula, and Mycieslki inequality and Fisher information was also satisfied for the different eigenstates. This study's findings have applications in quantum chemistry, atomic and molecular physics, and quantum physics.
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Abstract The Shannon entropy (S) and the Fisher Information (I) entropies are investigated for a generalized hyperbolic potential in position and momentum spaces. First, the Schrodinger equation is solved exactly using the Nikiforov‐Uvarov‐Functional Analysis method to obtain the energy spectra and the corresponding wave function. By Fourier transforming the position space wave function, the corresponding momentum wave function was obtained for the low‐lying states corresponding to the ground and first excited states. The positions and momentum of Shannon entropy and Fisher Information entropies were calculated numerically. Finally, the Bialynicki‐Birula and Mycielski and the Stam‐Cramer‐Rao inequalities for the Shannon entropy and Fisher Information entropies, respectively, were tested and were found to be satisfied for all cases considered.