Eigen solutions, Shannon entropy and fisher information under the Eckart Manning Rosen potential model

Onate, C. A.; Onyeaju, M. C.; Ikot, Akpan N.; Idiodi, J. O. A.; Ojonubah, J. O.

doi:10.3938/jkps.70.339

Cited by 24 publications

(11 citation statements)

References 36 publications

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“…Recent studies have focused on the combination of, at least, two potentials. The essence of combining two or more physical potential models is to take into account more physical phenomena into existing investigations of molecular physics [81][82][83][84][85].…”

Section: Introductionmentioning

confidence: 99%

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Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional analysis method

et al. 2022

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The energy levels of the Schrödinger equation under the Eckart-Hellmann potential (EHP) energy function are studied by the Nikiforov-Uvarov-Functional Analysis (NUFA) method. We obtained the analytic solution of the energy spectra and the wave function in closed form with the help of Greene-Aldrich approximation. The numerical bound states energy for various screening parameters at different quantum states and vibrational energies of EHP for CuLi, TiH, VH, and TiC diatomic molecules were computed. Four exceptional cases of this potential were achieved. To test the accuracy of our results, we computed the bound states energy eigenvalues of Hellmann potential which are in excellent agreement with the report of other researchers.

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Section: Introductionmentioning

confidence: 99%

“…The essence of joining at least two physical potential models is to take into account more physical application and comparative analysis to existing investigations of molecular physics [81][82][83][84][85].…”

Section: Introductionmentioning

confidence: 99%

Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional analysis method

et al. 2022

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“…The analytical solution of the Schrödinger equation with ℓ = 0 and ℓ ≠ 0 for some potentials has been addressed by many researchers in non-relativistic and relativistic quantum mechanics for bound states (Durmus and Yasuk, 2007;Edet et al, 2020d;2021b;Louis et al, 2018a;. Some of these potentials include Deng-Fan potential (Falaye et al, 2015), Hyperbolic potential (Onate et al, 2018b), Eckart potential (Onate et al, 2017), generalized trigonometric Pöschl-Teller potential (Edet et al, 2020e), and screened Kratzer Potential (Ikot et al, 2020a).…”

Section: Introductionmentioning

confidence: 99%

Effect of the deformation parameter on the nonrelativistic energy spectra of the q-deformed Hulthen-quadratic exponential-type potential

et al. 2021

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In this study, an approximate solution of the Schr�dinger equation for the q-deformed Hulthen-quadratic exponential-type potential model within the framework of the Nikiforov�Uvarov method was obtained. The bound state energy equation and the corresponding eigenfunction was obtained. The energy spectrum is applied to study H2, HCl, CO and LiH diatomic molecules. The effect of the deformation parameters and other potential parameters on the energy spectra of the system were graphically and numerically analyzed in detail. Special cases were considered when the potential parameters were altered, resulting in deformed Hulthen potential, Hulthen potential, deformed quadratic exponential-type potential and quadratic exponential-type potential. The energy eigenvalues expressions agreed with what obtained in literature. Finally, the results can find many applications in quantum chemistry, atomic and molecular physics.

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“…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

Int J of Quantum Chemistry

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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...

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Eigen solutions, Shannon entropy and fisher information under the Eckart Manning Rosen potential model

Cited by 24 publications

References 36 publications

Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional analysis method

Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional analysis method

Effect of the deformation parameter on the nonrelativistic energy spectra of the q-deformed Hulthen-quadratic exponential-type potential

Fisher information and uncertainty relations for potential family

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