Approximate Solutions Of The Non-Relativistic Schrődinger Equation With An Interaction Of Coulomb And Hulthѐn Potentials.

Onate, C. A.

doi:10.15764/tphy.2014.02011

Cited by 15 publications

(10 citation statements)

References 28 publications

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“…To obtain the solution of the Schrödinger-like equation given in Eq. 2, we write the radial Schrödinger equation of the form [15,41,43]…”

Section: Arbitrary -Solution To the Radial Schrödinger Equationmentioning

confidence: 99%

“…Arbitrary -solutions play a dominant role in non-relativistic quantum mechanics since the wave function and associated eigenvalues contain all the necessary information for a full description of a quantum system [5][6][7][8]. With the experimental verification of the Schrödinger equation, researchers have devoted much interest in solving the radial Schrödinger equation to obtain bound state solutions with various methods for some potential models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

2020

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In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.

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“…To obtain the solution of the Schrödinger-like equation given in Eq. 2, we write the radial Schrödinger equation of the form [15,41,43]…”

Section: Arbitrary -Solution To the Radial Schrödinger Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

2020

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“…with any of these exponential-type potentials are obtained using different methods which include: asymptotic iteration method (AIM) [10][11][12][13][14][15][16], Nikiforov-Uvarov (N.U) method [17][18][19][20], exact/ proper quantization rule [21], supersymmetric method [22][23][24][25][26][27], 1/N shifted expansion method [28], etc.…”

Section: Introductionmentioning

confidence: 99%

Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach

Onate

Ojonubah

2015

J Theor Appl Phys

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Using the basic concept of the supersymmetric shape invariance approach and formalism, we obtained an approximate solution of the Schrödinger equation with an interaction of inversely quadratic Yukawa potential, Yukawa potential and Coulomb potential which we considered as a class of Yukawa potentials. By varying the potential strengths, we obtained a solution for Hellmann potential, Yukawa potential, Coulomb potential and inversely quadratic Yukawa potential. The numerical results we obtained show that the interaction of these potentials is equivalent to each of the potential.

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“…In this work, we employ the parametric Nikiforov‐Uvarov method. To use this method, we first consider the differential equation of the form

([], \frac{d^{2}}{{italicdy}^{2}} + \frac{(c_{1} - c_{2})}{normaly ((), 1 - c_{3} normaly)} \frac{d}{dy} + \frac{- {Ay}^{2} + italicBy - C}{y^{2} {(1 - c_{3} y)}^{2}}) ψ ((), y) = 0 .

…”

Section: Eigensolutionmentioning

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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Approximate Solutions Of The Non-Relativistic Schrődinger Equation With An Interaction Of Coulomb And Hulthѐn Potentials.

Cited by 15 publications

References 28 publications

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach

Fisher information and uncertainty relations for potential family

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