The Fisher-information-based uncertainty relation, Cramer–Rao inequality and kinetic energy for the<i>D</i>-dimensional central problem

Dehesa, J. S.; González‐Férez, Rosario; Sánchez-Moreno, P.

doi:10.1088/1751-8113/40/8/011

Cited by 88 publications

(83 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The uncertainty properties are clearly delineated by the Stam inequalities [12]. The product F ρ F γ has been conjectured to exhibit a nontrivial lower bound [13] such that for 3-dimensional systems in the s state…”

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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…Nowadays it remains a strongly controversial problem [43][44][45][46][47][48][49]. First, it was conjectured [45] in 2000 that the position-momentum Fisher information product had the lower bound I 1 (ρ)I 1 (γ ) 4 for one-dimensional quantum systems with the position and momentum densities ρ(x) = | (x)| 2 and γ (p) = | (p)| 2 , (p) being the Fourier transform of (x).…”

Section: Introductionmentioning

confidence: 99%

Heisenberg-like and Fisher-information-based uncertainty relations forN-electrond-dimensional systems

et al. 2015

View full text Add to dashboard Cite

Heisenberg-like and Fisher-information-based uncertainty relations which extend and generalize previous similar expressions are obtained for N -fermion d-dimensional systems. The contributions of both spatial and spin degrees of freedom are taken into account. The accuracy of some of these generalized spinned uncertainty-like relations is numerically examined for a large number of atomic and molecular systems.

show abstract

“…Moreover, both measures (i) are closely related to fundamental and/or experimentally measurable quantities of finite electronic and nucle-onic systems [27][28][29][30][31][32], (ii) have been used to identify the most distinctive nonlinear phenomena (avoided crossings) encountered in atomic and molecular spectra under external fields [33,34], (iii) are the cornerstones of two alternative formulations of the classical thermodynamics [35,36], and (iv) satisfy the sharp inequalities [37][38][39][40] …”

Section: Introductionmentioning

confidence: 99%

Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states

Dehesa

López-Rosa

Martínez–Finkelshtein

et al. 2009

Int. J. Quantum Chem.

151

View full text Add to dashboard Cite

ABSTRACT:The analytic information theory of quantum systems includes the exact determination of their spatial extension or multidimensional spreading in both position and momentum spaces by means of the familiar variance and its generalization, the power and logarithmic moments, and, more appropriately, the Shannon entropy and the Fisher information. These complementary uncertainty measures have a global or local character, respectively, because they are power-like (variance, moments), logarithmic (Shannon) and gradient (Fisher) functionals of the corresponding probability distribution. Here we explicitly discuss all these spreading measures (and their associated uncertainty relations) in both position and momentum for the main prototype in D-dimensional physics, the hydrogenic system, directly in terms of the dimensionality and the hyperquantum numbers which characterize the involved states. Then, we analyze in detail such measures for s-states, circular states (i.e., single-electron states of highest angular momenta allowed within an electronic manifold characterized by a given principal hyperquantum number), and Rydberg states (i.e., states with large radial hyperquantum numbers n).

show abstract

The Fisher-information-based uncertainty relation, Cramer–Rao inequality and kinetic energy for theD-dimensional central problem

Cited by 88 publications

References 50 publications

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

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

Heisenberg-like and Fisher-information-based uncertainty relations forN-electrond-dimensional systems

Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states

Contact Info

Product

Resources

About