arXiv:1703.10042

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

O. Olendski

Published Mar 26, 2017• 1 citation

Abstract

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.

DOI: 10.48550/arxiv.1703.10042

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arXiv:1703.10042

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

O. Olendski

Published Mar 26, 2017• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.1703.10042

Related papers

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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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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.