Arbitrary ℓ-state solutions of the Klein-Gordon equation with the Manning-Rosen plus a Class of Yukawa potentials

Ahmadov, A. I.; Demirci, Mehmet; Aslanova, S. M.; Mustamin, M. F.

doi:10.1016/j.physleta.2020.126372

Cited by 52 publications

(11 citation statements)

References 55 publications

(73 reference statements)

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“…In the following, we obtain the energy level equation in ordinary quantum mechanics As seen from Equation (30), it is in a perfect agreement with the result obtained in Equation ( 27) of Ref. [49]. If we consider Equation ( 11) into Equation ( 30) and do some simple algebraic derivation, we can obtain the energy eigenvalue equation in the simplest form…”

Section: : ð29þsupporting

confidence: 79%

“…Unfortunately, for arbitrary l states (l ≠ 0), the KFG equation cannot get an exact solution with these potentials due to the centrifugal term of potentials. The numerous research works reveal the SUSY QM method's power and simplicity in solving wave equations of the central and noncentral potentials for arbitrary l states [42][43][44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

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Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

Ahmadov

Aslanova

Orujova

et al. 2021

Advances in High Energy Physics

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The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound state problem is the Klein-Fock-Gordon equation. In this work, using a developed scheme, we present how to surmount the centrifugal part and solve the modified Klein-Fock-Gordon equation for the linear combination of Hulthén and Yukawa potentials. In particular, we show that the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept. Here, both scalar potential conditions, which are whether equal and nonequal to vector potential, are considered in the calculation. The energy levels and corresponding normalized eigenfunctions are represented as a recursion relation regarding the Jacobi polynomials for arbitrary l states. Beyond that, a closed form of the normalization constant of the wave functions is found. Furthermore, we state that the energy eigenvalues are quite sensitive with potential parameters for the quantum states. The nonrelativistic and relativistic results obtained within SUSY QM overlap entirely with the results obtained by ordinary quantum mechanics, and it displays that the mathematical implementation of SUSY quantum mechanics is quite perfect.

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Section: : ð29þsupporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

Ahmadov

Aslanova

Orujova

et al. 2021

Advances in High Energy Physics

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“…( 87) and (91) into Eq. ( 90),and considering T 2 > 0 we obtain relation between parameters [64,49,65]…”

Section: Solution Of the Fh Equation For Thsckp Via Susyqm Methodsmentioning

confidence: 99%

Energy and momentum eigenspectrum of the Hulthén-screened cosine Kratzer potential using proper quantization rule and SUSYQM method

Purohit

Parmar²,

Kumar

2021

J Mol Model

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Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulth'en-screened cosine Kratzer potentials. For the suggested time independent Hulthén-screened cosine Kratzer potential, we solved the Schrödinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulth'en-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers (H 2 , I 2 , O 2 ) and heterodimers (M nH, ScN, LiH, HCl). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers M nH and ScN . The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer LiH, HCl and homodimer I 2 , O 2 , H 2 . The calculated energy and momentum spectra are tabulated and analysed.

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“…Therefore, we must use the improved approximation of the centrifugal term proposed by Badawi et al [71]; this method proved its power and efficiency when compared with the Greene and Aldrich approximation for a short-range potential [6]. Unlike the following approximation used in the previous work in QM and NCQM [17,18,59,60,62,72] :…”

Section: The Solution Of Dkge Under Modified Manning-rosen Potential In Rncqmmentioning

confidence: 99%

A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in RNCQM and NRNCQM symmetries

Maireche

2021

Rev. Mex. Fís.

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In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, the deformed Klein–Gordon and Schrödinger equations were solved with the modified equal vector scalar Manning-Rosen potential that has been of signiﬁcance interest in recent years using Bopp's shift method and standard perturbation theory in the first-order in the noncommutativity parameters in 3-dimensions noncommutative quantum mechanics. By employing the improved approximation of the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, and Ar2). The obtained energy eigenvalues appear as a function of the generalized Gamma function, the parameters of noncommutativity, and the parameters of studied potential, in addition to the atomic quantum numbers . In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result is consistent with what is obtained in the literature. We have seen that the improved approximation of the centrifugal term is better than the other approximations in ﬁnding the approximate analytical solutions of the Klein-Gordon and Schrödinger equations for the modified Manning–Rosen potential in RNCQM and NRNCQM.

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Arbitrary ℓ-state solutions of the Klein-Gordon equation with the Manning-Rosen plus a Class of Yukawa potentials

Cited by 52 publications

References 55 publications

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

Energy and momentum eigenspectrum of the Hulthén-screened cosine Kratzer potential using proper quantization rule and SUSYQM method

A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in RNCQM and NRNCQM symmetries

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