Bound state solutions of<i>d</i>-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential

Ikot, Akpan N.; Awoga, Oladunjoye A.; Antia, Akaninyene D.

doi:10.1088/1674-1056/22/2/020304

Cited by 29 publications

(18 citation statements)

References 37 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%

“…In this regard, it is important to notice that our proposal accepts, depending on the choice of the

α, β

, and

bold-italicγ

parameters, different approximations to

\frac{1}{r^{2}}

. For example, if

α = k^{2} ω,

β = k^{2} λ,

γ = 0

, and

k = {(2 α)}^{- 1}

one have

T_{normalc} = \frac{ω \exp (- 2 α r)}{1 - \exp (- 2 α r)} + \frac{λ \exp (- 2 α r)}{{(1 - \exp (- 2 α r))}^{2}} \approx \frac{1}{r^{2}}

that is the approximation used by Ikot et al Similarly, the choice of

α = ω

β = 0

γ = 1

, and

k = δ^{- 1}

leads to

T_{normalc} = \frac{ω δ^{2} \exp (- δ r)}{1 - \exp (- δ r)} + \frac{δ^{2} \exp (- 2 δ r)}{{(1 - \exp (- δ r))}^{2}}

…”

Section: Bound‐state Solutions Of D‐dimensional Schrödinger Equation mentioning

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%

“…In this regard, it is important to notice that our proposal accepts, depending on the choice of the

α, β

, and

bold-italicγ

parameters, different approximations to

\frac{1}{r^{2}}

. For example, if

α = k^{2} ω,

β = k^{2} λ,

γ = 0

, and

k = {(2 α)}^{- 1}

one have

T_{normalc} = \frac{ω \exp (- 2 α r)}{1 - \exp (- 2 α r)} + \frac{λ \exp (- 2 α r)}{{(1 - \exp (- 2 α r))}^{2}} \approx \frac{1}{r^{2}}

that is the approximation used by Ikot et al Similarly, the choice of

α = ω

β = 0

γ = 1

, and

k = δ^{- 1}

leads to

T_{normalc} = \frac{ω δ^{2} \exp (- δ r)}{1 - \exp (- δ r)} + \frac{δ^{2} \exp (- 2 δ r)}{{(1 - \exp (- δ r))}^{2}}

…”

Section: Bound‐state Solutions Of D‐dimensional Schrödinger Equation mentioning

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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“…It is well-known that SUSYQM allows one to determine the eigenvalues and eigenfunctions analytically for solvable potentials model using algebraic operator formulation without solving the Schrödinger-like differential equation by the standard series method. Many authors have in recent times solved the Schrodinger-like equation with physically motivated potential models [11][12][13][14][15]. The SUSYQM was first introduced by Witten [1] for the first time as a simplest supersymmetric model in quantum field theory.…”

Section: Introductionmentioning

confidence: 99%

Analytic solution of multi-dimensional Schrödinger equation in hot and dense QCD media using the SUSYQM method

Abu‐Shady

Ikot

2019

Eur. Phys. J. Plus

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The N-radial Schrödinger equation is analytically solved by using SUSYQM method, in which the heavy quarkonia potential is introduced at finite temperature and baryon chemical potential. The energy eigenvalue is calculated in the N-dimensional space. The obtained results show that the binding energy strongly decreases with increasing temperature and is slightly sensitive for changing baryon chemical potential up to 0.6 GeV at higher values of temperatures. We employed the nonperturbative corrections to the leading-order of the Debye mass at finite baryon chemical potential. We found that the binding energy is more dissociates when the nonperturbative corrections are included with the leading-order term of Debye mass in both hot and dense media. A comparison is discussed with other works such as the lattice parameterized of Debye mas. Thus, the present potential with the SUSYQM method provides satisfying results for the description of the dissociation of binding energy for heavy quarkonia in hot and dense media.

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“…Recently, most of the theoretical studies have been developed to study the solutions of radial Schrödinger equation in the higher dimensions. These studies are general and one can directly obtain the results in the lower dimensions [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The -dimensional Schrödinger equation has been solved by various methods as the Nikiforov-Uvarov (NU) method [9][10][11][12], asymptotic iteration method (AIM) [13], Laplace Transform method [14,15], supersymmetric quantum mechanics (SUSQM) [16], power series technique [17], Pekeris type approximation [18], and the analytical exact iteration method (AEIM) [19].…”

Section: Introductionmentioning

confidence: 99%

Binding Energies and Dissociation Temperatures of Heavy Quarkonia at Finite Temperature and Chemical Potential in theN-Dimensional Space

Abu‐Shady

Abdel-Karim

Khokha

2018

Advances in High Energy Physics

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The N-dimensional radial Schrödinger equation has been solved using the analytical exact iteration method (AEIM), in which the Cornell potential is generalized to finite temperature and chemical potential. The energy eigenvalues have been calculated in the N-dimensional space for any state. The present results have been applied for studying quarkonium properties such as charmonium and bottomonium masses at finite temperature and quark chemical potential. The binding energies and the mass spectra of heavy quarkonia are studied in the N-dimensional space. The dissociation temperatures for different states of heavy quarkonia are calculated in the three-dimensional space. The influence of dimensionality number (N) has been discussed on the dissociation temperatures. In addition, the energy eigenvalues are only valid for nonzero temperature at any value of quark chemical potential. A comparison is studied with other recent works. We conclude that the AEIM succeeds in predicting the heavy quarkonium at finite temperature and quark chemical potential in comparison with recent works.

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Bound state solutions ofd-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential

Cited by 29 publications

References 37 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

Analytic solution of multi-dimensional Schrödinger equation in hot and dense QCD media using the SUSYQM method

Binding Energies and Dissociation Temperatures of Heavy Quarkonia at Finite Temperature and Chemical Potential in theN-Dimensional Space

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