Publisher’s Note: “Exact solutions of deformed Schrödinger equation with a class of non-central physical potentials” [J. Math. Phys. 56, 062111 (2015)]

Based on the minimal length concept, inspired by Heisenberg algebra, a closed analytical formula is derived for the energy spectrum of the prolate γ-rigid Bohr-Mottelson Hamiltonian of nuclei, within a quantum perturbation method (QPM), by considering a scaled Davidson potential in β shape variable. In the resulting solution, called X(3)-D-ML, the ground state and the first β-band are all studied as a function of the free parameters. The fact of introducing the minimal length concept with a QPM makes the model very flexible and a powerful approach to describe nuclear collective excitations of a variety of vibrational-like nuclei. The introduction of scaling parameters in the Davidson potential enables us to get a physical minimum of this latter in comparison with previous works. The analysis of the corrected wave function, as well as the probability density distribution, shows that the minimal length parameter has a physical upper bound limit.

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“…To solve this differential equation via the asymptotic iteration method (AIM) [35,36], we propose the following ansatz:…”

Section: Treatment Of the Ordinary Cas α = 0 Within Aimmentioning

confidence: 99%

“…After calculating λ 0 and s 0 , by means of the recurrence relations of equation (2.3) given in Ref. [36], we get the generalized formula of the reduced energy from the roots of the quantization condition(Eq. (2.6) in Ref.…”

Section: Treatment Of the Ordinary Cas α = 0 Within Aimmentioning

confidence: 99%

Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method

et al. 2018

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“…As already mentioned, the asymptotic iteration method (AIM) [10,11] has been proposed and applied [16][17][18][19][20][21] to solve the second-order homogeneous differential equation of the form…”

Section: Overview Of the Asymptotic Iteration Methodsmentioning

confidence: 99%

Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model

Chabab

Lahbas

Oulne

2015

Int. J. Mod. Phys. E

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In the present work, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning-Rosen potential for γ−unstable nuclei as well as exactly separable rotational ones with γ ≈ 0. Some heavy nuclei with known β and γ bandheads have been fitted by using two parameters in the γ−unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.

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“…Very recently, we obtained general analytical solutions of Schrödinger equation in the context of position dependent effective mass for a class of non central physical potentials [66], involving in particular the Coulomb potential combined with several generalized versions forms of ring-shape such as double ring-shaped potential and novel angle-dependent (NAD) potential. The results of these calculations with non-central potentials may have interesting applications, particularly in quantum chemistry such as the study of ring-shaped molecules like cyclic polyenes and benzene [61].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, our aim in the present work, is to investigate analytical bound state solutions of the D-dimentional Schrödinger equation with a general deformed Woods-Saxon potential combined to double ring-shaped potential reported in [2,62,66], using the asymptotic iteration method.…”

Section: Introductionmentioning

confidence: 99%

Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential

Chabab

Batoul

Oulne

2015

Zeitschrift Für Naturforschung A

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By employing the Pekeris approximation, the D-dimensional Schrödinger equation is solved for the nuclear deformed Woods-Saxon potential plus double ring-shaped potential within the framework of the Asymptotic Iteration Method (AIM). The energy eingenvalues are given in a closed form and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric functions. Our general results reproduce many predictions obtained in the literature, using the Nikiforov-Uvarov method (NU) and the Improved Quantization Rule approach, particulary those derived by considering Woods-Saxon potential without deformation and/or without ring shape interaction.

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Publisher’s Note: “Exact solutions of deformed Schrödinger equation with a class of non-central physical potentials” [J. Math. Phys. 56, 062111 (2015)]

Cited by 9 publications

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Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method

Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method

Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model

Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential

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