Analytical Approximate Solution of Schrödinger Equation in
                    <i>D</i>
                    Dimensions with Quadratic Exponential-Type Potential for Arbitrary
                    <i>l</i>
                    -State

Ikot, Akpan N.; Awoga, Oladunjoye A.; Hassanabadi, H.; Maghsoodi, E.

doi:10.1088/0253-6102/61/4/09

Cited by 28 publications

(16 citation statements)

References 41 publications

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“…The Schrödinger equation given in eq. has been solved by different authors using specific methods for particular potentials; see for example, the papers of Ikot et al for the quadratic exponential‐type potential and for the Eckart plus modified deformed Hylleraas potentials, both solved by means of the Nikiforov–Uvarov method . With the same purpose, in the next section we present our alternative approach.…”

Section: Schrödinger Equation In D‐dimensionsmentioning

confidence: 99%

See 1 more Smart Citation

Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials

Peña

García‐Martínez

García-Ravelo

et al. 2014

Int J of Quantum Chemistry

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In this article, using an exactly‐solvable multiparameter exponential‐type potential we propose a unified treatment of the analytical bound—state solutions of the Schrödinger equation for exponential‐type potentials in D‐dimensions. Our proposal accepts different approximations to the centrifugal term; however, its usefulness is exemplified in the frame of the Green and Aldrich approach. This fact enables us to compare our results with specific potentials found in the literature and that are obtained here as particular cases of our proposal. That is, instead of solving a specific exponential‐type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are derived straightforward from the proposed approach. Furthermore, our proposal can be used as an alternative way in the search of solutions to new exponential‐type potentials besides that one can study different approximations to the term 1/r2. © 2014 Wiley Periodicals, Inc.

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Section: Schrödinger Equation In D‐dimensionsmentioning

confidence: 99%

“…Consequently, eqs. (18)(19)(20) ensure that the potential VðrÞ is attractive with an infinite wall in r s . Besides, due to the fact that the potential given in eq.…”

Section: A Class Of Multiparameter Exponential-type Potentialmentioning

confidence: 99%

Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials

Peña

García‐Martínez

García-Ravelo

et al. 2014

Int J of Quantum Chemistry

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“…In its standard form (non deformed), the Quadratic Exponential‐type potential was proposed by Ikot et al as

V^{Q} ((), r) = V_{0} ((), \frac{a + {italicbe}^{- αr} + {italicce}^{- 2 αr)}}{{(1 - e^{- αr})}^{2}})

where V 0 , a , b , c , α are constants. The corresponding q ‐deformed Quadratic Exponential‐type potential is achieved if one selects A ( q ) = V 0 c ( q ),

B = V_{0} ((), c ((), q) + \frac{b ((), q)}{q})

C = V_{0} \frac{a ((), q)}{q^{2}}, k = \frac{1}{α}

in Equation , then

\begin{matrix} lefttrue \\ V (r) = \frac{V_{0} c (q) q e^{- α (r - r_{e})}}{1 - {italicqe}^{- α (r - r_{e})}} + \frac{V_{0} (qc (q) + b (q)) e^{- α (r - r_{e})}}{{(1 - {italicqe}^{- α (r - r_{e})})}^{2}} \\ + \frac{V_{0} c (q) e^{- α 2 (r - r_{e})}}{{(1 - {italicqe}^{- α (r - r_{e})})}^{2}} \end{matrix}

such that…”

Section: Some Useful Applicationsmentioning

confidence: 99%

Approximate ℓ‐bound state solutions of q‐deformed exponential‐type potentials

Peña

García-Ravelo

Ovando

et al. 2020

Int J of Quantum Chemistry

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In this work, the exactly solvable Schrödinger equation for s-states of a class of multiparameter exponential-type potential (E-tP) is used to obtain the approximate ℓ 6 ¼ 0 bound state solutions for the corresponding q-deformed radial potentials. To deal with the effective potential, the Pekeris approximation for the centrifugal term is applied. The proposal has the advantage that, depending on the choice of the parameters involved in the E-tP, several q-deformed exponential potentials are obtained here as particular cases. That is, our proposition indicates that it is not necessary to use specialized methods to solve the Schrödinger equation for specific q-deformed exponential potentials. At this regard, in order to show the usefulness of the proposed method, we consider the ℓ 6 ¼ 0 bound state solutions of the q-deformed Tietz, Hulthén, Manning-Rosen, Shioberg, quadratic exponential, Wei and Hua among other potential models. Furthermore, with the example of the Hua potential we are contributing to solve the recent controversy on the energy spectra of this q-deformed model. Moreover, in some applications considered in this work the results can be used to correct similar findings already published. Besides, the proposal is useful when considering new q-deformed potentials with hypergeometric wavefunctions to be used in quantum chemical applications of diatomic molecules. K E Y W O R D Sℓ 6 ¼ 0 bound-state solutions, exponential-type models, Pekeris approximation, q-deformed potentials, Schrödinger equation

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“…These higher dimensional studies provide a general treatment of the problem in such a manner that one can obtain the required results in lower dimensions just dialing appropriate D. Many analytical as well as numerical techniques like the Laplace transform method [21][22][23], the Nikiforov-Uvarov method [24], the algebraic method [25], the 1 N expansion method [26], the path integral approach [27], the SUSYQM [28], the exact quantization rule [29] and others are applied to address Schrödinger equation both for lower and higher dimensional cases. In addition to that, hyperbolic potentials, exponential-type potentials or their combinations have attracted a lot of interest of different authors [30][31][32][33][34][35][36], both for multidimensional and lower dimensional Schrödinger equation. Bound state solutions of these potentials are very important in literature as they describe the different phenomenon like scattering, vibrational properties of molecules.…”

Section: Introductionmentioning

confidence: 99%

Analytical approximate bound state solution of Schrödinger equation in D -dimensions with a new mixed class of potential for arbitrary ℓ-state via asymptotic iteration method

Das¹

2016

Chinese Journal of Physics

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The bound state solutions of the D-dimensional Schrödinger equation for new mixed class of potential, V (r) = V 1 r 2 + V 2 e −αr r + V 3 cothαr + V 4 , are studied within the framework of the Pekeris approximation for any arbitrary ℓ-state. Asymptotic iteration method (AIM) is used for the work.The energy spectrum are obtained as well as their corresponding normalized eigenfunctions are derived in terms of generalized hypergeometric functions 2 F 1 (a, b, c; z). It is shown that using the Pekeris approximation, present potential model is very much capable of deriving other well known potentials quite easily and corresponding solutions are in excellent agreement with the previous work carried out in literature.

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Analytical Approximate Solution of Schrödinger Equation in D Dimensions with Quadratic Exponential-Type Potential for Arbitrary l -State

Cited by 28 publications

References 41 publications

Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials

Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials

Approximate ℓ‐bound state solutions of q‐deformed exponential‐type potentials

Analytical approximate bound state solution of Schrödinger equation in D -dimensions with a new mixed class of potential for arbitrary ℓ-state via asymptotic iteration method

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