Asymptotic iteration approach to supersymmetric bistable potentials

Çiftçi, Hakan; Özer, Okan; Roy, Provas Kumar

doi:10.1088/1674-1056/21/1/010303

Cited by 6 publications

(4 citation statements)

References 34 publications

(17 reference statements)

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“…Unfortunately, it could only be possible for a very limited number of potentials such as harmonic oscillators, Coulomb, Kratzer potentials and so on [16] with a centrifugal term for l = 0. In this way, there are several established analytical methods, including Polynomial solution [16,18,19], Nikiforov-Uvarov method (NU) [20], Supersymmetric quantum mechanics method (SUSY QM) [21,22], and Asymptotic iteration method (AIM) [23][24][25][26][27][28][29], in order to solve analytically the radial Schrödinger equation for l = 0 within various potentials. G.Levai et al suggested a simple method for the proposed potentials for which the Schrödinger equation can be solved exactly with special functions [30] and presented relationship between the introduced formalism and supersymmetric quantum mechanics [21].…”

Section: Introductionmentioning

confidence: 99%

Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

2019

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In this paper, the approximate analitical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are found for any angular momentum case via the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSY QM) methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transformed each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well V 0 and W , the radial n r and l orbital quantum numbers and parameters D, a, R 0 are also identified in detail. Finally, the bound state energies and the corresponding normalized hyper-radial wave functions for the neutron system of the a 56 F e nucleus are calculated in D = 2 and D = 3, as well as the energy spectrum expressions of other highest dimensions are identified by using the energy spectrum of D = 2 and D = 3.

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Section: Introductionmentioning

confidence: 99%

Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

2019

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“…Along the years, there was a huge amount of research effort to solve exactly the radial Schrödinger equation for all values of n r and l quantum numbers, but it could only be possible for a few specific potentials. In this way, there are several established analytical methods, including Polynomial solution [1][2][3], Nikiforov -Uvarov method (NU) [4], Supersymmetric quantum mechanics method (SUSYQM) [5,6], and Asymptotic iteration method (AIM) [7][8][9][10][11][12][13], to solve the radial Schrödinger equation exactly or quasi-exactly for l = 0 within these potentials. G.Levai et al suggested a simple method for the proposed potentials for which the Schrödinger equation can be solved exactly with special functions [14] and presented relationship between the introduced formalism and SUSYQM [5].…”

Section: Introductionmentioning

confidence: 99%

The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

Badalov

2016

Int. J. Mod. Phys. E

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In this work, the analytical solutions of the D-dimensional Schrödinger equation are studied in great detail for the Wood-Saxon potential by taking advantage of the Pekeris approximation.Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential V 0 , the radial n r and orbital l quantum numbers and parameters D, a, R 0 are defined as well.

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“…In this study we will apply a new formalism based on the Taylor series expansion method, namely, asymptotic Taylor expansion method (ATEM) [22], to bistable potentials. These type of potentials have been used in the quantum theory of molecules as a crude model to describe the motion of a particle in the presence of two centers of force [23][24][25][26][27][28][29]. It is mentioned in [22] that the taylor series Method [30,31] is an old one but it has not been fully exploited in the analysis of both physical and mathematical problems in solution.…”

Section: Introductionmentioning

confidence: 99%

Application of the Asymptotic Taylor Expansion Method to Bistable Potentials

Özer

Koklu

Resitoglu

2013

Advances in Mathematical Physics

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A recent method called asymptotic Taylor expansion (ATEM) is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.

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Asymptotic iteration approach to supersymmetric bistable potentials

Cited by 6 publications

References 34 publications

Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

Application of the Asymptotic Taylor Expansion Method to Bistable Potentials

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