Analytical solutions of position-dependent mass Klein–Gordon equation for unequal scalar and vector Yukawa potentials

Wang, Z.; Long, Zheng-Wen; Long, Chao-Yun; Wang, L. Z.

doi:10.1007/s12648-015-0677-9

Cited by 14 publications

(8 citation statements)

References 60 publications

(60 reference statements)

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“…This result is in good agreement with the expression obtained in Equation (A.3) of Ref [58]. Furthermore, this result is also the same with the expression for the constant mass case obtained in Ref [67]. One can easily see this by setting q=1 and α → δ in Equation (39) of Ref [67] (iv) Also, if V 0 = −S 0 , and…”

Section: Resultssupporting

confidence: 89%

“…and this result is the same with Equation (A.2) of Ref [67] (vi) If we take l = 0 (the s-wave case), the centrifugal term in Equation ( 9) disappears because 4lðl + 1Þδ 2 e −2δr / ð1 − e −2δr Þ 2 = 0 and the equation turns to the s -wave KFG equation. By setting l = 0 in Equation ( 31), its energy spectrum equation is the following form:…”

Section: Resultssupporting

confidence: 82%

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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: Resultssupporting

confidence: 89%

Section: Resultssupporting

confidence: 82%

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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show abstract

“…( 52) of Ref: [58]. Furthermore, this result is also the same with the expression for the constant mass case obtained in Ref: [67]. One can easily see this by setting q=1 and α → δ in Eq.…”

Section: Resultssupporting

confidence: 85%

“…One can easily see this by setting q=1 and α → δ in Eq. ( 39) of Ref: [67]. iv) Also, if V 0 = −S 0 , and…”

Section: Resultsmentioning

confidence: 99%

Analytical bound-state solutions of the Klein-Fock-Gordon equation for the sum of Hulthén and Yukawa potential within SUSY quantum mechanics

Ahmadov¹,

Aslanova²,

Orujova³

et al. 2021

Preprint

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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 non-equal 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 non-relativistic 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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“…Among them, the NU and SUSYQM methods have received great interest. By using these two techniques, many works have been conducted to obtain either exact or approximate solutions of the KG equation with some well-known potentials as follows: Manning-Rosen Potential [23,24,25], Yukawa potential [26,27,28], Hulthen Potential [29,30,31], generalized Hulthen potential [32,33,34], Kratzer Potential [35], Wood-Saxon Potential [36,37,38] and Deng-Fan molecular potentials [39]. Similarly for the case of combined potentials: ManningRosen plus Hulthn potential [40], Hulthn plus a Ring-Shaped like potential [41], Hulthn plus Yukawa potential [42] and references in there [43].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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Focusing on an improved approximation scheme, we present how to treat the centrifugal and the Coulombic behavior terms and then to obtain the bound state solutions of the Klein-Gordon (KG) equation with the Manning-Rosen plus a Class of Yukawa potentials. By means of the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods, we present the energy spectrum for any ℓ-state and the corresponding radial wave functions in terms of the hypergeometric functions. From both methods we obtain the same results. Several special cases for the potentials which are useful for other physical systems are also discussed. These are consistent with those results in previous works. We obtain that the energy level E is sensitive to the potential parameter δ at fixed values of other parameters and increases when δ runs from 0.05 to 0.3. Furthermore, E is sensitive to the quantum numbers ℓ and n r for a given δ, as expected.

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Analytical solutions of position-dependent mass Klein–Gordon equation for unequal scalar and vector Yukawa potentials

Cited by 14 publications

References 60 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

Analytical bound-state solutions of the Klein-Fock-Gordon equation for the sum of Hulthén and Yukawa potential within SUSY quantum mechanics

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

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