Entropy, Fisher Information and Variance with Frost-Musulin Potenial

In this research work, the quantum information‐theoretic analysis of the static screened Coulomb potential has been carried out by studying both analytically and numerically the entropic measures, Fisher information as well as the Onicescu information energy of its wave function. Explicit expressions of these information‐theoretic measures were obtained. Using the Srivastava–Daoust linearization formula in terms of the multivariate Lauricella hypergeometric function, the Rényi entropy, Tsallis entropy, Onicescu information energy were analytically obtained. From the results obtained, it is observed that some of the Shannon entropies are negative, indicating that, negative entropies exists for the probability densities that are highly localized. The trends in the variation of the information‐theoretic measures with the potential screening parameter a for this atomic model are discussed. The Bialynicki‐Birula, Mycielski inequality (BBM), and the Fisher information based uncertainty relation are also verified.

Section: Introductionmentioning

confidence: 99%

“…The Shannon entropy is defined in the position and momentum spaces as:

S_{r} = - \int_{c}^{b} ρ (r) \ln ρ (r) d r

and

S_{p} = - \int_{c}^{b} ρ (p) \ln ρ (p) d p,

where S r is the position space Shannon entropy, S p is the momentum space Shannon entropy,

ρ (r) = {true| ψ (r) true|}^{2}

and

ρ (p) = {true| ψ (p) true|}^{2}

are the probability densities in the position and momentum spaces, respectively. ψ( p ) denotes the wave function in the momentum coordinate obtained by the Fourier transform of ψ( r ).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Quantum information‐theoretic measures for the static screened Coulomb potential

Isonguyo

Oyewumi

Oyun

2018

“…[28,29], authors have demonstrated the same relations for CHA. Further, I was explored for vibrational levels of various diatomic model potentials, such as Pöschl-Teller, [39] pseudo-harmonic, [40] Tietz-Wei, [41] Frost-Musulin, [42] Generalized Morse, [43] and exponential-cosine screened coulomb potential. [44] The exact analytical form of I in conjugate r, p space for 3D FHO was reported in Ref.…”

mentioning

confidence: 99%

Fisher information in confined isotropic harmonic oscillator

Mukherjee

Roy

2018

Fisher information (I) is investigated in a confined harmonic oscillator (CHO) enclosed in a spherical enclosure, in conjugate r and p spaces. A comparative study between CHO and a free quantum particle in spherical box (PISB), as well as CHO and respective free harmonic oscillator (FHO) is pursued with respect to energy spectrum and I. This reveals that, a CHO offers two exactly solvable limits, namely, a PISB and an FHO. Moreover, the dependence of I on quantum numbers n r, l, m in FHO and CHO are analogous. The role of force constant is discussed. Further, a thorough systematic analysis of I with respect to variation of confinement radius r c is presented, with particular attention on nonzero‐(l, m) states. Considerable new important observations are recorded. The results are quite accurate and most of these are presented for the first time.

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...