The quasi-exactly solvable potentials method applied to the three-body problem

Chafa, F.; Chouchaoui, A.; Hachemane, M.; Ighezou, F.-Z.

doi:10.1016/j.aop.2006.07.007

Cited by 8 publications

(5 citation statements)

References 16 publications

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“…In other to find energy eigenvalues and the wave function (eigensolution) of the secondorder homogeneous linear differential equations of the above form, there have been several eigensolution techniques developed to exactly solve the quantum systems. Some of these techniques include the AIM [29,30,[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], the Feynman integral formalism [51][52][53], FAA [54][55][56][57][58][59], the exact quantization rule method [60][61][62][63][64][65], the proper quantization rule [66,67], the Nikiforov-Uvarov method [68][69][70][71][72][73][74][75][76][77][78], SU...…”

Section: Eigensolution Techniquesmentioning

confidence: 99%

Eigensolution techniques, their applications and Fisherʼs information entropy of the Tietz–Wei diatomic molecular model

Falaye¹,

Oyewumi²,

Ikhdair³

et al. 2014

Phys. Scr.

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In this study, approximate analytical solution of Schrödinger, Klein-Gordon and Dirac equations under the Tietz-Wei (TW) diatomic molecular potential are represented by using an approximation for the centrifugal term. We have applied three types of eigensolution techniques; the functional analysis approach (FAA), supersymmetry quantum mechanics (SUSYQM) and asymptotic iteration method (AIM) to solve Klein-Gordon, Dirac and Schrödinger equations, respectively. The energy eigenvalues and the corresponding eigenfunctions for these three wave equations are obtained and some numerical results and figures are reported. It has been shown that these techniques yielded exactly same results. some expectation values of the TW diatomic molecular potential within the framework of the Hellmann-Feynman theorem (HFT) have been presented. The probability distributions which characterize the quantum-mechanical states of TW diatomic molecular potential are analyzed by means of complementary information measures of a probability distribution called the Fishers information entropy. This distribution has been described in terms of Jacobi polynomials, whose characteristics are controlled by the quantum numbers.

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Section: Eigensolution Techniquesmentioning

confidence: 99%

Eigensolution techniques, their applications and Fisherʼs information entropy of the Tietz–Wei diatomic molecular model

Falaye¹,

Oyewumi²,

Ikhdair³

et al. 2014

Phys. Scr.

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show abstract

“…Several mathematical approaches have been developed to solve differential equations arising from these considerations. They include the supersymmetric approach [21][22][23][24], Nikiforov-Uvarov method [25][26][27], asymptotic iteration method (AIM) [28][29][30], Feynman integral formalism [31][32][33][34], factorization formalism [35,36], Formula Method [37] exact quantization rule method [38][39][40][41][42][43], proper quantization rule [44][45][46][47][48], Wave Function Ansatz Method [49] etc... The trigonometric Pöschl-Teller potential was proposed by Pöschl and Teller [50] in 1933, and it has been used in describing diatomic molecular vibration.…”

Section: Introductionmentioning

confidence: 99%

Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

et al. 2020

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Analytical solutions of the Schrödinger equation for the generalized trigonometric Pöschl–Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the partition function was calculated and other relevant thermodynamic properties. More so, we use the concept of the superstatistics to also evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter and this is displayed graphically for the clarity of our results. We also obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the hypergeometric functions. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Pöschl–Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods

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“…Up to now, several approaches have been developed for tackling equation of form (1). This include the asymptotic iteration method (AIM) , Feynman integral formalism [26][27][28], functional analysis method [24,[29][30][31], exact quantization rule method [32][33][34][35][36][37], proper quantization rule [38][39][40], Nikiforov-Uvarov (NU) method [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57], supersymetric quantum mechanics [24,[58][59][60][61][62][63], the generalized pseudospectral method [64][65][66][67][68][69], etc. Notes on these techniques can be found in our recent work…”

Section: Introductionmentioning

confidence: 99%

“…Up to now, several approaches have been developed for tackling equation of form (1). This include the asymptotic iteration method (AIM) , Feynman integral formalism [26][27][28],…”

Section: Introductionmentioning

confidence: 99%

Formula Method for Bound State Problems

2014

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We present a simple formula for finding bound state solution of any quantum wave equation which can be simplified to the form of Ψ ′′ (s)The two cases where k 3 = 0 and k 3 = 0 are studied. We derive an expression for the energy spectrum and the wave function in terms of generalized hypergeometric functions 2 F 1 (α, β; γ; k 3 s). In order to show the accuracy of this proposed formula, we resort to obtaining bound state solutions for some existing eigenvalue problems in a rather more simplified way. This method has shown to be accurate, efficient, reliable and very easy to use particularly when applied to vast number of quantum potential models.

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The quasi-exactly solvable potentials method applied to the three-body problem

Cited by 8 publications

References 16 publications

Eigensolution techniques, their applications and Fisherʼs information entropy of the Tietz–Wei diatomic molecular model

Eigensolution techniques, their applications and Fisherʼs information entropy of the Tietz–Wei diatomic molecular model

Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

Formula Method for Bound State Problems

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