Non-relativistic eigensolutions of molecular and heavy quarkonia interacting potentials via the Nikiforov Uvarov method

Omugbe, E.

doi:10.1139/cjp-2020-0039

Cited by 23 publications

(21 citation statements)

References 43 publications

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“…(28) and (29) into (27), we obtained the expression (30) Finally, using the respective notations and given in Eqs. (17)(18)(19), we obtained the energy eigenvalue expression for the KPIQP as (31)…”

Section: Solution Of the Radial Schrodinger Equationmentioning

confidence: 99%

Mass Spectrum of Mesons via the WKB Approximation Method

Omugbe

Osafile

Onyeaju

2020

Advances in High Energy Physics

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In this paper, we demonstrated that the multiple turning point problems within the framework of the Wentzel-Kramers-Brillouin (WKB) approximation method can be reduced to two turning point one for a nonsymmetric potential function by using an appropriate Pekeris-type approximation scheme. We solved the Schrödinger equation with the Killingbeck potential plus an inversely quadratic potential (KPIQP) function. The special cases of the modeled potential are discussed. We obtained the energy eigenvalues and the mass spectra of the heavy QQ¯ and heavy-light Qq¯ mesons systems. The results in this present work are in good agreement with the results obtained by other analytical methods and available experimental data in the literature.

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Section: Solution Of the Radial Schrodinger Equationmentioning

confidence: 99%

Mass Spectrum of Mesons via the WKB Approximation Method

Omugbe

Osafile

Onyeaju

2020

Advances in High Energy Physics

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“…There are several studies with the Cornell potential in literature. For instance, Flores [9,30] studied the Schrödinger equation with the Cornell potential using variational method and supersymmetric quantum mechanics [9,10,[30][31][32]. Bruni et al [8] calculated the energy configuration for a quark-antiquark pair from the Nambu-Goto action.…”

Section: Introductionmentioning

confidence: 99%

“…It was shown that this configuration energy has the shape of a Cornell potential [8]. Khoka et al [31,33] utilized the analytical exact iterative method to solve N-dimensional Schrödinger equation with an extended Cornell potential [31]. They found the energy and mass spectrum of heavy quarkonia [31].…”

Section: Introductionmentioning

confidence: 99%

“…Khoka et al [31,33] utilized the analytical exact iterative method to solve N-dimensional Schrödinger equation with an extended Cornell potential [31]. They found the energy and mass spectrum of heavy quarkonia [31]. Omugbe [31] applied the Nikiforov-Uvarov method to obtain the eigensolutions of the radial Schrödinger equation with Cornell potential plus an inversely quadratic potential [11,31,34].…”

Section: Introductionmentioning

confidence: 99%

“…They found the energy and mass spectrum of heavy quarkonia [31]. Omugbe [31] applied the Nikiforov-Uvarov method to obtain the eigensolutions of the radial Schrödinger equation with Cornell potential plus an inversely quadratic potential [11,31,34]. Until now, an analysis of such states in quantum phase space via the Wigner function is still lacking.…”

Section: Introductionmentioning

confidence: 99%

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Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Luz

Petronilo

et al. 2022

Advances in High Energy Physics

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In this paper, we study within the structure of Symplectic Quantum Mechanics a bidimensional nonrelativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which consists of Coulomb-type plus linear potentials. First, we solve the Schrödinger equation in the phase space with the linear potential. The solution (ground state) is obtained and analyzed by means of the Wigner function related to Airy function for the c c ¯ meson. In the second case, to treat the Schrödinger-like equation in the phase space, a procedure based on the Bohlin transformation is presented and applied to the Cornell potential. In this case, the system is separated into two parts, one analogous to the oscillator and the other we treat using perturbation method. Then, we quantized the Hamiltonian with the aid of stars operators in the phase space representation so that we can determine through the algebraic method the eigenfunctions of the undisturbed Hamiltonian (oscillator solution), and the other part of the Hamiltonian was the perturbation method. The eigenfunctions found (undisturbed plus disturbed) are associated with the Wigner function via Weyl product using the representation theory of Galilei group in the phase space. The Wigner function is analyzed, and the nonclassicality of ground state and first excited state is studied by the nonclassicality indicator or negativity parameter of the Wigner function for this system. In some aspects, we observe that the Wigner function offers an easier way to visualize the nonclassic nature of meson system than the wavefunction does phase space.

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Approximate solutions for diatomic molecules under combined potentials in a global monopole and Aharonov–Bohm flux field

Nayek,

Dutta,

Pradhan

2024

Int J of Quantum Chemistry

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Bound state energy eigensolutions of nine different diatomic molecules, specifically, , TiH, , CO, NO, ScH, CrH, HCl and LiH, placed in a point‐like global monopole, have been calculated by solving the time‐independent Schrödinger equation (SE). The molecules are confined by the Aharonov–Bohm (AB) flux field and the interaction potential among the charged particles is governed by the combined screened modified Kratzer potential (SMKP) plus Hulthén potential model. Three other special cases of the interaction potential have also been discussed here. Asymptotic iteration method has been used for the mathematical calculations. It is difficult to solve the SE exactly for any non‐zero values of the azimuthal quantum number due to the presence of the centrifugal barrier term. The well‐known Pekeris approximation technique for the terms and has taken into consideration for the purpose of performing numerical computations connected to an arbitrary state. The outcomes of this study are in reasonable agreement with the results of previous research on SMKP, Kratzer‐Fues potential, and modified Kratzer potential in the Minkowski space. It is observed that the energy spectra of the diatomic molecules suffer considerable change due to the effects of the background AB‐flux field and topological defect parameter.

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Non-relativistic eigensolutions of molecular and heavy quarkonia interacting potentials via the Nikiforov Uvarov method

Cited by 23 publications

References 43 publications

Mass Spectrum of Mesons via the WKB Approximation Method

Mass Spectrum of Mesons via the WKB Approximation Method

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Approximate solutions for diatomic molecules under combined potentials in a global monopole and Aharonov–Bohm flux field

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