The Fisher information of single-particle systems with a central potential

Romera, E.; Sánchez-Moreno, P.; Dehesa, J. S.

doi:10.1016/j.cplett.2005.08.032

Cited by 179 publications

(185 citation statements)

References 27 publications

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“…F γ 0 a=0 = 48. This result is greater than the lower bound c F = 36 of the Fisher-based uncertainty relation (10). For all values of the atomic number the results for F ρc F γc are greater than the corresponding results for F ρ0 F γ 0 .…”

Section: Results For Shannon Entropy and Fisher Informationmentioning

confidence: 41%

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Shannon entropies and Fisher information of K-shell electrons of neutral atoms

Sekh¹,

Saha

Talukdar

2018

Physics Letters A

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We represent the two K-shell electrons of neutral atoms by Hylleraas-type wave function which fulfils the exact behavior at the electron-electron and electron-nucleus coalescence points and, derive a simple method to construct expressions for single-particle position-and momentum-space charge densities, ρ(r) and γ(p) respectively. We make use of the results for ρ(r) and γ(p) to critically examine the effect of correlation on bare (uncorrelated) values of Shannon information entropies (S) and of Fisher information (F ) for the K-shell electrons of atoms from helium to neon. Due to inter-electronic repulsion the values of the uncorrelated Shannon position-space entropies are augmented while those of the momentum-space entropies are reduced. The corresponding Fisher information are found to exhibit opposite behavior in respect of this. Attempts are made to provide some plausible explanation for the observed response of S and F to electronic correlation.

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Section: Results For Shannon Entropy and Fisher Informationmentioning

confidence: 41%

“…(6) and (7) belong to position-and momentum-spaces respectively. Equations (6) and (7) can be written in the equivalent forms [10] …”

Section: Shannon Entropy and Fisher Information For Many-electronmentioning

confidence: 99%

Shannon entropies and Fisher information of K-shell electrons of neutral atoms

Sekh¹,

Saha

Talukdar

2018

Physics Letters A

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“…Contrary to the quantum entropies, which always obey the lower bound from Eq. (16), similar universal relation between position and momentum components of the Fisher information is not known though for several particular systems some inequalities have been derived [52][53][54][55][56]. In quantum mechanics, one of its main applications is due to the fact that it enters into the expression for the kinetic energy of the manyparticle system [57] and in this way establishes the link between, for example, density functional methods and information theory.…”

Section: Introductionmentioning

confidence: 99%

“…In quantum mechanics, one of its main applications is due to the fact that it enters into the expression for the kinetic energy of the manyparticle system [57] and in this way establishes the link between, for example, density functional methods and information theory. Due to its importance, a research on the Fisher information and its relation to the quantum entropy is a very vigorous one and it discovers a lot of the new results [40,54,[58][59][60][61][62][63][64][65][66][67]. For our subsequent analysis, we provide here easily derivable expressions for the position and momentum Fisher informations of the bound state of the negative Robin wall:…”

Section: Introductionmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Olendski

2016

Annalen der Physik

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Information-theoretical concepts are employed for the analysis of the interplay between a transverse electric field E applied to a one-dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length Λ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position Sx and momentum S k quantum information entropies and their Fisher information Ix and I k and Onicescu information energies Ox and O k counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, Λ = 0 (Neumann, Λ = ∞), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum-information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field-independent sum Sx + S k . Analogously, at Λ = 0 and Λ = ∞ the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as E 2/3 (E 1/3 ) and its inverse, respectively, leading to the field-independent product IxI k (OxO k ). Peculiarities of their transformations at the finite nonzero Λ are discussed and similarities and differences between the three quantum-information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

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“…Following the work of López-Rosa et al 1 as well as Romera et al, 2 Fisher information in both position and momentum spaces for hydrogenic atoms has analytical expressions for arbitrary (n,l,m) states…”

Section: Crámer-rao Complexitymentioning

confidence: 99%