arXiv:1703.03405 · European Journal of Physics

Comment on ‘On the realisation of quantum Fisher information’

O. Olendski

Published Mar 8, 2017• 3 citations

Abstract

Abstract It is shown that calculation of the momentum Fisher information of the quasi-one-dimensional hydrogen atom recently presented by Saha et al (2017 Eur. J. Phys. 38 025103 ) is wrong. A correct derivation is provided and its didactical advantages and scientific significances are highlighted.

DOI: 10.1088/1361-6404/aa62cd

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A further argument is provided in the discussion on the correct form of the bound-state momentum wave function of the quasi-one-dimensional hydrogen atom; namely, considering its behavior at the large quantum indices, it is reconfirmed that the complex expression from Olendski (2017) {\it Eur. J. Phys.} {\bf 38} 038001 is a correct one. Groundlessness of other interpretations is also highlighted.

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arXiv:1703.03405 · European Journal of Physics

Comment on ‘On the realisation of quantum Fisher information’

O. Olendski

Published Mar 8, 2017• 3 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1361-6404/aa62cd

Related papers

Comment on 'Fisher information for quasi-one-dimensional hydrogen atom'

O. Olendski

arXiv:1703.10042Mar 26, 20171 citation

Comment on ‘Solving a singular integral equation for the one-dimensional Coulomb problem’ (2023 Physica Scripta 98 085219)

Yu-Peng Zhang, Qihao Zeng, Dong Sun +1 more

Abstract It is shown by Olendski that the derivation of the momentum waveform of the quasi-one-dimensional hydrogen atom recently performed by Shutovskyi et al (2023 Phys. Scr. 98 085 219) contains the same error as in the previous effort by Saha et al (2017 Eur. J. Phys. 38 025 103). The error was also identified by Olendski (2017 Eur. J. Phys. 38 038 001; 2019 Eur. J. Phys. 40 025 402). To exemplify the faulty nature of Shutovski et al formula, the standard deviations of position and momentum that enter the Heisenberg uncertainty relation were calculated. It produced different results in the position and wave vector spaces, whereas the use of the correct expression yields the same value by either method.Abstract It is shown by Olendski that the derivation of the momentum waveform of the quasi-one-dimensional hydrogen atom recently performed by Shutovskyi et al (2023 Phys. Scr. 98 085 219) contains the same error as in the previous effort by Saha et al (2017 Eur. J. Phys. 38 025 103). The error was also identified by Olendski (2017 Eur. J. Phys. 38 038 001; 2019 Eur. J. Phys. 40 025 402). To exemplify the faulty nature of Shutovski et al formula, the standard deviations of position and momentum that enter the Heisenberg uncertainty relation were calculated. It produced different results in the position and wave vector spaces, whereas the use of the correct expression yields the same value by either method.

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Fisher information for quasi-one-dimensional hydrogen atom

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The coordinate-space wave function $ψ(x)$ of quasi-one-dimensional atoms is defined in the $x\geq 0$ region only. This poses a typical problem to write a physically acceptable momentum-space wave function $ϕ(p)$ from the Fourier transform of $ψ(x)$ . We resolve the problem with special attention to the behavior of real and imaginary parts of the complex-valued function $ϕ(p)$ as a function of $p$ and confirm that $ϕ_i(p)$ (the imaginary part of $ϕ(p)$ ) represents the correct momentum-space wave function. We make use of the results for $ψ(x)$ and $ϕ_i(p)$ to express the position- and momentum-space Fisher information in terms of the principal quantum number and energy eigen value of the system and provide some useful checks on the result presented with particular attention on the information theoretic uncertainty relation.The coordinate-space wave function $ψ(x)$ of quasi-one-dimensional atoms is defined in the $x\geq 0$ region only. This poses a typical problem to write a physically acceptable momentum-space wave function $ϕ(p)$ from the Fourier transform of $ψ(x)$. We resolve the problem with special attention to the behavior of real and imaginary parts of the complex-valued function $ϕ(p)$ as a function of $p$ and confirm that $ϕ_i(p)$ (the imaginary part of $ϕ(p)$) represents the correct momentum-space wave function. We make use of the results for $ψ(x)$ and $ϕ_i(p)$ to express the position- and momentum-space Fisher information in terms of the principal quantum number and energy eigen value of the system and provide some useful checks on the result presented with particular attention on the information theoretic uncertainty relation.

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Abstract With special attention to the role of information theory in physical sciences we present analytical results for the coordinate- and momentum-space Fisher information of some important one-dimensional quantum systems which differ in spacing of their energy levels. The studies envisaged allow us to relate the coordinate-space information ( I ρ ) with the familiar energy levels of the quantum system. The corresponding momentum-space information ( I γ ) does not obey such a simple relationship with the energy spectrum. Our results for the product ( I ρ I γ ) depend quadratically on the principal quantum number n and satisfy an appropriate uncertainty relation derived by Dehesa et al (2007 J. Phys. A: Math. Theor. 40 1845 )Abstract With special attention to the role of information theory in physical sciences we present analytical results for the coordinate- and momentum-space Fisher information of some important one-dimensional quantum systems which differ in spacing of their energy levels. The studies envisaged allow us to relate the coordinate-space information ( I ρ ) with the familiar energy levels of the quantum system. The corresponding momentum-space information ( I γ ) does not obey such a simple relationship with the energy spectrum. Our results for the product ( I ρ I γ ) depend quadratically on the principal quantum number n and satisfy an appropriate uncertainty relation derived by Dehesa et al (2007 J. Phys. A: Math. Theor. 40 1845 )

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

C. A. Onate, M. C. Onyeaju

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.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.

International Journal of Quantum ChemistryMar 10, 20210 citations

The coordinate-space wave function

ψ(x)

of quasi-one-dimensional atoms is defined in the

x\geq 0

region only. This poses a typical problem to write a physically acceptable momentum-space wave function

ϕ(p)

from the Fourier transform of

ψ(x)

. We resolve the problem with special attention to the behavior of real and imaginary parts of the complex-valued function

ϕ(p)

as a function of

p

and confirm that

ϕ_i(p)

(the imaginary part of

ϕ(p)

) represents the correct momentum-space wave function. We make use of the results for

ψ(x)

and

ϕ_i(p)

to express the position- and momentum-space Fisher information in terms of the principal quantum number and energy eigen value of the system and provide some useful checks on the result presented with particular attention on the information theoretic uncertainty relation.