Relativistic Study of the Spinless Salpeter Equation with a Modified Hylleraas Potential

Antia, Akaninyene D.; Okon, I. B.; Umoren, E. B.; Isonguyo, Cecilia N.

doi:10.15407/ujpe64.1.27

Cited by 7 publications

(4 citation statements)

References 23 publications

(31 reference statements)

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“…However, the study of information theory of quantummechanical systems have been extensively used in recent years to study a variety of quantum mechanical systems (Majernik, et al, 1996;Yanez, et al, 1994;Dehesa, et al, 1997;Dehesa, et al, 2006;Yahya, et al, 2014a;Yahya, et al, 2014b;Yahya, et al, 2013;Osobonye, et al, 2020;Patil, et al, 2007;Isonguyo, et al, 2018;Okon, et al, 2018 andAntia, et al, 2018). This is because, it provides a deeper knowledge into the internal structure of the quantum systems and it is closely related with modern quantum computation and information, which is a basic theory for numerous technological developments (Gadre, et al, 1991 andNielson, 2001).…”

Section: Introductionmentioning

confidence: 99%

Entropic uncertainty relations and the fisher information for the Generalized radial Yukawa potential

Isonguyo¹,

Oyewumi²,

Oyun³

et al. 2023

wojast

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The Heisenberg uncertainty relation as well as the Fisher information are presented analytically and numerically for the Generalized radial Yukawa potential. The probability density for the ground and first excited state has been analyzed via the Fisher information for this potential model. Some numerical results are obtained. From the numerical results obtained, we observed that, for n = 0, 1, the position-space Fisher information Ir increases with increasing potential parameter a, while the momentum-space Fisher information Iρ initially increases, and later decreases with increasing potential parameter a. The Fisher-information-based uncertainty relation and the Heisenberg uncertainty relation have been verified to hold for this atomic model. In addition, we observed a squeezed phenomenon in some of the results in position r and momentum ρ for the ground and first excited states.

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Section: Introductionmentioning

confidence: 99%

Entropic uncertainty relations and the fisher information for the Generalized radial Yukawa potential

Isonguyo¹,

Oyewumi²,

Oyun³

et al. 2023

wojast

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show abstract

“…The Greene-Aldrich approximation scheme is mostly applicable for short range potentials [7]. Eigensolutions for both relativistic and nonrelativistic wave equations have been studied with different methods which include the following: Exact quantisation, WKB, Nikiforov-Uvarov method (NU), Laplace transform technique, asymptotic iteration method, proper quantisation, supersymmetric quantum mechanics approach, vibrational approach, formula method, factorisation method, and Shifted 1/N-expansion method [8][9][10][11][12][13]. Bound state solutions obtained from the Schrödinger equation has practical applications in investigating tunnelling rate of quantum mechanical systems [14] and mass spectra of quarkonia systems [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

Okon

Onate

Omugbe

et al. 2022

Advances in High Energy Physics

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In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential). The proposed potential is best suitable for smaller values of the screening parameter α . The resulting energy eigenvalue is presented in a close form and extended to study thermal properties and superstatistics expressed in terms of partition function Z and other thermodynamic properties such as vibrational mean energy U , vibrational specific heat capacity C , vibrational entropy S , and vibrational free energy F . Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtained for various values of the screening parameter ( α ) as well as different expectation values via Hellmann-Feynman Theorem (HFT). The trend of the partition function and other thermodynamic properties obtained for both thermal properties and superstatistics were in excellent agreement with the existing literatures. Due to the analytical mathematical complexities, the superstatistics and thermal properties were evaluated using Mathematica 10.0 version software. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential, and Coulomb potential as special cases.

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“…Most potentials are modelled and applied to solve some physical systems examples include: Morse potential, Tietz-Wei, pseudoharmonic, Deng-Fan, Kratzer -Feus, Mie-Type and many of exponential -type potentials [9][10][11][12][13][14][15]. Most of the hyperbolic and trigonometric potentials are applicable in nuclear and high energy physics [16][17]. Most recently, some physical potential has been modelled in trigonometric and hyperbolic potential well.…”

Section: Introductionmentioning

confidence: 99%

Eigen-Solutions to Schrodinger Equation with Trigonometric Inversely Quadratic Plus Coulombic Hyperbolic Potential

Okon

Antia

Akankpo

et al. 2020

PSIJ

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In this work, we applied parametric Nikiforov-Uvarov method to analytically obtained eigen solutions to Schrodinger wave equation with Trigonometric Inversely Quadratic plus Coulombic Hyperbolic Potential. We obtain energy-Eigen equation and total normalised wave function expressed in terms of Jacobi polynomial. The numerical solutions produce positive and negative bound state energies which signifies that the potential is suitable for describing both particle and anti-particle. The numerical bound state energies decreases with an increase in quantum state with fixed orbital angular quantum number 0, 1, 2 and 3. The numerical bound state energies decreases with an increase in the screening parameter and 0.5. The energy spectral diagrams show unique quantisation of the different energy levels. This potential reduces to Coulomb potential as a special case. The numerical solutions were carried out with algorithm implemented using MATLAB 8.0 software using the resulting energy-Eigen equation.

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Relativistic Study of the Spinless Salpeter Equation with a Modified Hylleraas Potential

Cited by 7 publications

References 23 publications

Entropic uncertainty relations and the fisher information for the Generalized radial Yukawa potential

Entropic uncertainty relations and the fisher information for the Generalized radial Yukawa potential

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

Eigen-Solutions to Schrodinger Equation with Trigonometric Inversely Quadratic Plus Coulombic Hyperbolic Potential

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