Quantum information‐theoretic measures for the static screened Coulomb potential

Accurate values of physical quantities serve as the stepping stone for further researches. Consequently, we provide benchmark values of Shannon, Rényi, Tsallis entropies, and Onicescu information energy for ground state helium. With the highly correlated Hylleraas wave functions, our calculations fully considered the effect of electron correlation. Presented numerical results converge with increasing size of basis set, fulfill analytic relations between the quantities, and satisfactorily agree with those in the literature. In particular, we present these information‐theoretic quantities with high accuracy, and it is believed that the reported data would be a valuable reference for further research on information‐theoretic quantities of atomic and molecular systems.

mentioning

confidence: 99%

Benchmark calculations of Rényi, Tsallis entropies, and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

2019

“…The momentum expectation value 〈 p 2 〉 is given by

(〈〉, p^{2}) = 2 π {|m|}^{2} \int_{0}^{\infty} R_{italicEn normalℓ}^{2} ((), r) italicdr \int_{0}^{π} \frac{{(||, Y_{normalℓ m} ((),, θ, ϕ))}^{2}}{\sin θ} italicdθ, = \frac{1}{2} ((), 2 normalℓ + 1) (||, m) (〈〉, r^{- 2}),

where

\int_{0}^{π} \frac{{(||, Y_{normalℓ m} ((),, θ, ϕ))}^{2}}{\sin θ} italicdθ = \frac{2 normalℓ + 1}{4 (||, m)},

and

(〈〉, r^{- 2}) = \int_{0}^{\infty} R_{italicEn normalℓ}^{2} ((), r) italicdr,

this after some algebraic manipulation yields

(〈〉, p^{2}) = \frac{V_{3} \sqrt{2 μ}}{ℏ} ((), normalℓ + 2 n + \frac{1}{4} \sqrt{{(1 + 2 ℓ)}^{2} + \frac{8 μ V_{1}}{{normalℏ}^{2}}}) + \frac{V_{2}}{2 ((), n + normalℓ)} .

…”

Section: Fisher Informationmentioning

confidence: 99%

“…Thus, several authors have reported the computation for Fisher information for different physical potential models. Among the works reported are: Fisher information and variance with Frost‐Musulin potential, Fisher information‐based uncertainty relation, Cramer‐Rao inequality and kinetic energy for the D‐dimensional central problem, information and complexity measures for the ring‐shaped modified Kratzer potential, Fisher information for position‐dependent mass Schrödinger system, quantum information‐theoretic measures for the static screened Coulomb potential, Fisher information of a single‐particle system with a central potential, Fisher information and complexity measure of generalized Morse potential model, Eigen solutions, Shannon entropy and Fisher information under Eckart Manning‐Rosen potential model, Eigensolution techniques, their applications and Fisher's information entropy of the Tietz‐Wei diatomic molecular model, Fisher information in confined hydrogen‐like ions, Fisher information in confined isotropic harmonic oscillator, Fisher information and complexity measure of Generalized Morse potential model, Shannon and Fisher entropy measures for a parity‐restricted harmonic oscillator, radial position‐momentum uncertainties for the infinite circular well and Fisher entropy, quantum information measures of infinite spherical well . In this study, the authors aimed at investigating the solutions of the radial Schrödinger equation and Fisher information confined in a potential family which is proposed in the course of this study.…”

Section: Introductionmentioning

confidence: 99%

Fisher information and uncertainty relations for potential family

Onate

Onyeaju

Ikot

et al. 2019

An approximate bound state solution of the three-dimensional Schrödinger equation for potential family was obtained together with the corresponding wave function, after which the Fisher information for a potential family was explicitly obtained via the methodology of expectation value and radial expectation value. Some uncertainty relations that are closely related to Heisenberg-like uncertainty were obtained and numerical results were generated to justify the relations and inequalities. Finally, we have numerically studied the Fisher information for two special cases from the result of the potential family that has applications to prototype systems. It was deduced that the Fisher information of the potential family and that of the two special cases exhibit similar features.bound state solutions, expectation value, Fisher information, potential term, uncertainty relations 1 | INTRODUCTION A particle in a D-dimensional spherical box is one of the basic fundamental ideas of quantum physics such as the effect of boundary condition and quantization energy. A particle confined in a quantum system exhibits a distinguishable change in both the physical and chemical properties. [1,2] According to Laguna and Sagar, [3] the confined quantum-mechanical models have proved to be suitable first approximations for establishing the effect of pressure on the spectral lines of atoms and molecules. Thus, the behavior of confined systems with different potential models required vigorous attention because of its applications such as in quantum dots, astrophysics, condensed matter and semiconductor physics. [4][5][6] A onedimensional confined Harmonic Oscillator model has been studied in connection with the effect of distant boundaries on the energy level, [7,8] effect on the separation of variables, [9] information entropies in position space [10] and energies and Einstein coefficients. [11] Similarly, in the introductory courses of quantum mechanics, several models proposed were useful for the discussion of semiclassical approaches, variational methods, and perturbation theory. Motivated by this, the authors aimed to study the Fisher information of a particle subjected to a system confined in a potential family.Fisher information introduced in the theory of statistical estimation is the main theoretic tool of the extreme physical information principle that allows numerous derivations of fundamental equations of physics. [12][13][14][15] Fisher information is the gradient functional of probability density, which is a local measure as it is sensitive to local rearrangements of the density. The higher the Fisher information, the smaller the uncertainty in a system. This gives a higher accuracy in predicting the localization of a particle. Fisher information has been shown to be closely connected with other density functional that characterizes a number of microscopic properties of fundamental character as well as physical observables. [16,17] This, however, results to the formulation of uncertainty relations that is stronger than the C...

“…On the other hand, Fisher information, being the sole component of the local measure, is primarily concerned with local changes that occur in probability density. [ 18–20 ] The study of Fisher information finds its significance in density functional. [ 21–23 ] Fisher information entropy, defined as probability density in position and momentum spaces, is expressed as follows [ 11,12 ] :

I_{r} = \int \frac{{([], ρ' ((), \overset{false⇀}{r}))}^{2}}{ρ ((), \overset{false⇀}{r})} d \overset{r}{true} = 4 \int {|ψ' (\overset{r}{true})|}^{2} italicdr = 4 (〈〉, p^{2}) - 2 ((), 2 l + 1) (||, m) (〈〉, r^{- 2})

I_{p} = \int \frac{{([], ρ' ((), \overset{false⇀}{p}))}^{2}}{ρ ((), \overset{false⇀}{p})} d \overset{p}{true} = 4 \int {|ψ' (\overset{p}{true})|}^{2} italicdp = 4 (〈〉, r^{2}) - 2 ((), 2 l + 1) (||, m) (〈〉, p^{- 2})

…”

Section: Introductionmentioning

confidence: 99%

“…Generally, quantum information‐theoretic measures have been used to explore many areas of molecular, atomic, and reactive systems. [ 28–32 ] Recently, Isonguyo et al [ 20 ] , Yanez‐Navarro et al [ 33 ] and Pooja et al [ 34 ] studied the characteristic quantum information theory for screened Coulomb and Eckart potential models in one dimension, respectively. Many authors have investigated the quantum information for harmonic oscillators in one, two, and three dimensions [ 35,36 ] ; a single‐particle system with central potentials [ 11 ] ; and the shape and effect for quantum heterostructures, [ 37 ] pseudoharmonic potential, [ 38 ] hyperbolic well, [ 39 ] Tangent well, [ 40 ] Kratzer potential, [ 41 ] and many other potential models.…”

Section: Introductionmentioning

confidence: 99%

Shannon entropy and Fisher information for screened Kratzer potential

Amadi

Ikot

Ngiangia

et al. 2020

In this paper, Shannon entropy and Fisher information is studied for the screened Kratzer potential model and compared with the screened Coulomb in three dimensions. Our results showed similar higher-order characteristic behavior for position and momentum space. Our numerical results showed that increases in the accuracy of predicting particle location occurred in the position space. Our result shows that the sum of the position and momentum entropies satisfies the lower-bound Berkner, Bialynicki-Birula, and Mycieslki inequality. The Stam-Cramer-Rao inequalities relation for Fisher information and the expectation values were also satisfied for the different eigenstates. K E Y W O R D S expectation values, Fisher information, screened coulomb potential, screened Kratzer potential, Shannon entropy