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International Journal of Quantum Chemistry

Reply to the comment on “Fisher information of a vector potential for time‐dependent Feinberg–Horodecki”

C. A. Onate, M. C. Onyeaju

Published Mar 10, 2021• 0 citations
Publisher

Abstract

Nascimento et al. Commented and faulted the calculations on the article title “Fisher information of a vector potential for time-dependent Feinberg–Horodecki” by Onate and Onyeaju. The authors claimed that the calculations in the paper of Onate and Onyeaju (Reference [1]) of Nascimento et al carried several problems. Their main claimed is on Equation (3) of their Reference [1]. The authors went further to obtain a quantized momentum equation with their claim as the correct equation. They also have other claims in the calculations. These authors further faulted Reference [1] of their comment for citing wrong reference. Nascimento and co also said that Equation (21) of their Reference [1] is dimensionally wrong, this is not true. It is their Equation (9) that is dimensionally wrong. This also makes other equations that depends on Equation (9) in their claim to be wrong.

DOI
10.1002/qua.26632

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Onate and Onyeaju have recently studied the Feinberg–Horodecki equation with a special time-dependent Mie-type pseudoharmonic potential. They claim that the wavefunctions, quantized momentum and Fisher information have been obtained. We show in this comment that the results obtained in Onate and Onyeaju [1] carry several calculation problems that are corrected here. In order to show that the errors made in Onate and Onyeaju [1] are not just due to wrong choices of the constants x and a, we solve the Feinberg–Horodecki equation with a pseudoharmonic-type potential, that is, the Equation (5). After that, we use its solutions to calculate the different properties studied in Onate and Onyeaju [1]. In Figure 1, we show the plots of <t2>, <p2>, I(ρ) and I(γ) as function of te for the ground state of the system. Despite the fact that we have obtained <t2>, <p2> and I(ρ) analytically, we calculated I(γ) numerically. As we can see, <t2> (<p2>) increases (decreases) as te increases. On the other hand, I(ρ) (I(γ)) decreases (increases) with the increasing te. Those behaviors were also observed by the authors in Onate and Onyeaju [1]. However, since the expressions for <t2>, <p2> and I(ρ) presented in Onate and Onyeaju [1] are not correct, the numerical values of the curves and tables presented in Onate and Onyeaju [1] are also incorrect. In Figure 3 we show the plot of the product I(ρ)I(γ) for the ground state of the system as function of te. We observed that I(ρ)I(γ) ≥ 4 = 4D2, where D is the dimension of the problem (D = 1). This is a remarkable result which agree with the work by Sanchez-Moreno et al. [18], valid when either ψ(t) or ϕ(p) is real. In summary, we have shown several mistakes in the article by Onate and Onyeaju [1] in their calculations and showed the correct expressions for the quantized momentum, wavefunctions, mean values (<t2> and <p2>) and Fisher information. We show that Stam inequalities are satisfied (Figure 2) and that the product of Fisher information has a non-trivial lower bound (I(ρ)I(γ) ≥ 4). We hope that our results will be useful in providing new insights in the field of quantum chemistry. The authors are grateful to the National Counsel of Scientific and Technological Development (CNPq) and to the National Council for the Improvement of Higher Education (CAPES) of Brazil for financial support. Raimundo N. Costa Filho is supported by CNPq grant number 312384/2018-1.

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Nascimento et al. Commented and faulted the calculations on the article title “Fisher information of a vector potential for time-dependent Feinberg–Horodecki” by Onate and Onyeaju. The authors claimed that the calculations in the paper of Onate and Onyeaju (Reference [1]) of Nascimento et al carried several problems. Their main claimed is on Equation (3) of their Reference [1]. The authors went further to obtain a quantized momentum equation with their claim as the correct equation. They also have other claims in the calculations. These authors further faulted Reference [1] of their comment for citing wrong reference. Nascimento and co also said that Equation (21) of their Reference [1] is dimensionally wrong, this is not true. It is their Equation (9) that is dimensionally wrong. This also makes other equations that depends on Equation (9) in their claim to be wrong.
Onate and Onyeaju have recently studied the Feinberg–Horodecki equation with a special time-dependent Mie-type pseudoharmonic potential. They claim that the wavefunctions, quantized momentum and Fisher information have been obtained. We show in this comment that the results obtained in Onate and Onyeaju [1] carry several calculation problems that are corrected here. In order to show that the errors made in Onate and Onyeaju [1] are not just due to wrong choices of the constants x and a, we solve the Feinberg–Horodecki equation with a pseudoharmonic-type potential, that is, the Equation (5). After that, we use its solutions to calculate the different properties studied in Onate and Onyeaju [1]. In Figure 1, we show the plots of <t2>, <p2>, I(ρ) and I(γ) as function of te for the ground state of the system. Despite the fact that we have obtained <t2>, <p2> and I(ρ) analytically, we calculated I(γ) numerically. As we can see, <t2> (<p2>) increases (decreases) as te increases. On the other hand, I(ρ) (I(γ)) decreases (increases) with the increasing te. Those behaviors were also observed by the authors in Onate and Onyeaju [1]. However, since the expressions for <t2>, <p2> and I(ρ) presented in Onate and Onyeaju [1] are not correct, the numerical values of the curves and tables presented in Onate and Onyeaju [1] are also incorrect. In Figure 3 we show the plot of the product I(ρ)I(γ) for the ground state of the system as function of te. We observed that I(ρ)I(γ) ≥ 4 = 4D2, where D is the dimension of the problem (D = 1). This is a remarkable result which agree with the work by Sanchez-Moreno et al. [18], valid when either ψ(t) or ϕ(p) is real. In summary, we have shown several mistakes in the article by Onate and Onyeaju [1] in their calculations and showed the correct expressions for the quantized momentum, wavefunctions, mean values (<t2> and <p2>) and Fisher information. We show that Stam inequalities are satisfied (Figure 2) and that the product of Fisher information has a non-trivial lower bound (I(ρ)I(γ) ≥ 4). We hope that our results will be useful in providing new insights in the field of quantum chemistry. The authors are grateful to the National Counsel of Scientific and Technological Development (CNPq) and to the National Council for the Improvement of Higher Education (CAPES) of Brazil for financial support. Raimundo N. Costa Filho is supported by CNPq grant number 312384/2018-1.
Abstract The time‐dependent Feinberg–Horodecki equation in the presence of a special Mie‐type pseudoharmonic potential was solved and the quantized momentum with the corresponding wave functions were obtained with the supersymmetric approach. The Fisher information for both the time and the momentum space were calculated via expectation values of time and momentum. The effect of the dissociation energy, the equilibrium time point and the quantum number respectively on the Fisher information were studied in detail. The result was applied to five molecules. The results obtained for the time‐dependent Feinberg–Horodecki equation followed the trend of the results obtained for the time‐independent Schrödinger equation.
We obtain the quantized momentum eigenvalues Pn together with space-like coherent eigenstates for the space-like counterpart of the Schrödinger equation, the Feinberg–Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.