Construction of solvable non-central potential using vector superpotential: a new approach

Parmar, Rajendrasinh H.

doi:10.1007/s12648-019-01401-1

Cited by 19 publications

(14 citation statements)

References 31 publications

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“…Considering extremity conditions for wave functions, we obtain G > 0 and F < 0. Solving Equation (19) yields…”

Section: Bound State Solution Of the Radial Klein-mentioning

confidence: 99%

“…The Nikiforov-Uvarov method [8], factorization method [9], Laplace transform approach [10], and the path integral method [11] and shifted 1/N expansion approach [12,13] are used for solving radial and azimuthal parts of the wave equations exactly or quasiexactly in l ≠ 0 for various potentials. Additionally, there are numerous interesting research works about the KFG equation with physical potentials by using different methods in the literature [14][15][16][17][18][19][20][21][22][23][24][25][26]. Among them, as an example, in Ref.…”

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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“…Considering extremity conditions for wave functions, we obtain G > 0 and F < 0. Solving Equation (19) yields…”

Section: Bound State Solution Of the Radial Klein-mentioning

confidence: 99%

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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show abstract

“…To solve the various potentials, a variety of strategies are available. The asymptotic iteration method (AIM) [1,2], the ansatz method [3], the Nikiforov-Uvarov (NU) technique [4,5], the factorization technique [6,7], the formula method [8], and the supersymmetric quantum mechanics (SUSYQM) [9,10]. Furthermore, many quantization approaches exist to address potential issues.…”

Section: Introductionmentioning

confidence: 99%

“…In quantum physics, It is applied to describe the interactions of molecular structure. The KP has been widely used both in relativistic and non-relativistic regime in three or higher dimensions using various methods [4,5,9,10,6,7,1,8,2,11,3,12,13,14,15,16,17,22].…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

Purohit

PARMAR²,

Kumar

2021

Preprint

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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 Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-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 ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ 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.

show abstract

Construction of solvable non-central potential using vector superpotential: a new approach

Cited by 19 publications

References 31 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

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

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