Formula Method for Bound State Problems

Falaye, Babatunde J.; Ikhdair, Sameer M.; Hamzavi, Majid

doi:10.1007/s00601-014-0937-9

Cited by 72 publications

(66 citation statements)

References 80 publications

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“…It is asymptotic to a finite value as → ∞ and becomes infinite at = 0. [51] solved this potential within the framework of the proper quantization rule and eigenfunction was obtained via the Formula Method [52].The generalized inverse quadratic Yukawa potential model is of the form [51] ( ) = − 1 (1 + − ) 2 (1) [48] Compared the behaviour of the Yukawa-type potential with the Yukawa potential and the IQY potential for screening parameter values, it was noted that differences do not exist between these three potentials.…”

Section: Introductionmentioning

confidence: 99%

Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential

Edet

Okoi

Chima

2020

Rev. Bras. Ensino Fís.

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This study presents the solutions of Schrödinger equation for the Non-Central Generalized Inverse Quadratic Yukawa Potential within the framework of Nikiforov-Uvarov. The radial and angular part of the Schrödinger equation are obtained using the method of variable separation. More so, the bound states energy eigenvalues and corresponding eigenfunctions are obtained analytically. Numerical results were obtained for the Generalized Inverse Quadratic Yukawa Potential for comparison sake. It was found out that our results agree with existing literature.

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Section: Introductionmentioning

confidence: 99%

Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential

Edet

Okoi

Chima

2020

Rev. Bras. Ensino Fís.

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“…Considering equation (32a) with reference to [1], k 1 , k 2 , k 3 , A T −H , B T −H and C T −H can be found. Then, parameters k 4 and k 5 can be obtained as…”

Section: Calculation Of the Eigenfunctionsmentioning

confidence: 99%

“…3 E-mail: majid.hamzavi@gmail.com 1 past years, various eigensolution techniques have been proposed to solve quantum potential models. Few of these methods are: formula method [1], Nikiforov-Uvarov method [2], the asymptotic iteration method [3], the supersymmetric quantum mechanics [4], the factorization method [5], wave function ansatz method [6], the generalized pseudospectral method (GPS) [7] and the exact quantization rule (EQR) [8,9,10]. Notes on these techniques can be found in ref.…”

Section: Introductionmentioning

confidence: 99%

Spectroscopic study of some diatomic molecules via the proper quantization rule

Falaye

Ikhdair²,

Hamzavi

2015

J Math Chem

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Spectroscopic techniques are very essential tools in studying electronic structures, spectroscopic constants and energetic properties of diatomic molecules. These techniques are also required for parametrization of new method based on theoretical analysis and computational calculations. In this research, we apply the proper quantization rule in spectroscopic study of some diatomic molecules by solving the Schrödinger equation with two solvable quantum molecular systems-Tietz-Wei and shifted DengFan potential models for their approximate nonrelativistic energy states via an appropriate approximation to the centrifugal term. We show that the energy levels can be determined from its ground state energy. The beauty and simplicity of the method applied in this study is that, it can be applied to any exactly as well as approximately solvable models. The validity and accuracy of the method is tested with previous techniques via numerical computation for H 2 and CO diatomic molecules. The result also include energy spectrum of 5 different electronic states of NO and 2 different electronic state of ICl.

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“…Following the procedure described in ref. [26], we can write the solution U nℓ (t) in terms of hypergeometric polynomials and thus, the wave function takes the form…”

Section: The Eigenfunctionsmentioning

confidence: 99%

Shifted Tietz–Wei oscillator for simulating the atomic interaction in diatomic molecules

2015

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The shifted Tietz-Wei (sTW) oscillator is as good as traditional Morse potential in simulating the atomic interaction in diatomic molecules. By using the Pekeris-type approximation to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schrödinger equation with this typical molecular model via the exact quantization rule (EQR). The energy spectrum for a set of diatomic moleculesfor arbitrary values of n and ℓ quantum numbers are obtained. For the sake of completeness, we study the corresponding wavefunctions using the formula method.

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Formula Method for Bound State Problems

Cited by 72 publications

References 80 publications

Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential

Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential

Spectroscopic study of some diatomic molecules via the proper quantization rule

Shifted Tietz–Wei oscillator for simulating the atomic interaction in diatomic molecules

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