Comment on “Fisher information of a vector potential for time‐dependent Feinberg–Horodecki equation”

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 , , I(ρ) and I(γ) as function of te for the ground state of the system. Despite the fact that we have obtained , and I(ρ) analytically, we calculated I(γ) numerically. As we can see, () 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 , 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 ( and ) 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.