Analytical solutions of the Klein–Gordon equation with a combined potential

Onate, C. A.; Onyeaju, M. C.; Ikot, Akpan N.; Ojonubah, J. O.

doi:10.1016/j.cjph.2016.08.007

Cited by 33 publications

(17 citation statements)

References 50 publications

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“…The solution of the Schrödinger equation contains all the necessary information needed for the full description of a quantum state such as the probability density and entropy of the system 7,8 . The Schrödinger equation with many physical potentials model have been investigated in recent times with different advance mathematical technique such as Nikiforov-Uvarov (NU) method [9][10][11] , asymptotic iteration method (AIM) [12][13][14][15][16] , functional analysis approach 16 , supersymmetric quantum mechanics (SUSYQM) [17][18][19][20] among others 21 . One of such potential models is the Kratzer potential 22 where D is the dissociation energy and a is the equilibrium internuclear length.…”

Section: Introductionmentioning

confidence: 99%

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

et al. 2020

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In this paper, we obtained the exact bound state energy spectrum of the Schrödinger equation with energy dependent molecular Kratzer potential using asymptotic iteration method (AIM). The corresponding wave function expressed in terms of the confluent hypergeometric function was also obtained. As a special case, when the energy slope parameter in the energy-dependent molecular Kratzer potential is set to zero, then the well-known molecular Kratzer potential is recovered. Numerical results for the energy eigenvlaues are also obtained for different quantum states, in the presence and absence of the energy slope parameter. These results are discussed extensively using graphical representation. Our results are seen to agree with the results in literature.

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Section: Introductionmentioning

confidence: 99%

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

et al. 2020

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“…Substituting Eqs. (15)(16)(17)(18) into Eq. (10), we obtain the solution of the wave function ψ(Z) as:…”

Section: Solutions Of the Schrödinger Equation In D-dimensionsmentioning

confidence: 99%

“…Different methods employed over the years in obtaining these solutions include Nikiforov-Uvarov (NU) method [9][10][11][12], Supersymmetry quantum mechanics (SUSYQM) [13][14][15][16], Asymptotic iteration methos (AIM) [17], Proper and exact quantization rule [18][19], Factorization method [20], Functional Analysis Approach FAA (also known here as Modified Factorization Method) [21], etc. The modified factorization method is usually used to transform a secondorder homogeneous linear differential equation into a hypergeometric equation, with the help of a transformation scheme [22].…”

Section: Introductionmentioning

confidence: 99%

A study of thermodynamic properties of quadratic exponential-type potential in D-dimensions

et al. 2018

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We solved the Schrodinger equation with Quadratic Exponential-Type Potential (QEP) model in D-dimensions using the Modified factorization method. The energy eigenvalues and total wavefunctions were obtained in a Gauss hypergeometric form. The thermodynamic properties including vibrational partition function, vibrational mean energy, vibrational mean free energy and vibrational entropy have been calculated for the electronic state of (X1 Σ +g) Rubidium (Rb2) dimer. The QEP discussed can be applied extensively in Physics and Chemistry, especially in molecular dynamics.

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“…The Schrödinger equation with many physical potentials model have been investigated in recent times with different analytical methods such as Nikiforov-Uvarov (NU) method [5][6][7][8] , asymptotic iteration method (AIM) [9][10][11][12][13][14] , supersymmetric quantum mechanics(SUSYQM) [15][16][17][18] among others [19][20][21][22] . One of such potential models is the screened Coulomb potential, which is given by Eq.…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions of the Schrödinger equation with energy-dependent screened Coulomb potential in D – dimensions

et al. 2020

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Within the framework of the conventional Nikiforov-Uvarov method and a new form of Greene-Aldrich approximation scheme, we solved the Schrödinger equation with the energy-dependent screened Coulomb potential. Energy eigenvalues and energy eigenfunctions were obtained both approximately and numerically at different dimensions. The energy variations with different potential parameters, quantum numbers and energy slope parameter, respectively were also discussed graphically. The major finding of this research is the effect of the energy slope parameter on the energy spectra, which is seen in the existence of two simultaneous energy values for a particular quantum state. Our special cases also agree with the results obtained from literature, when the energy slope parameter is zero.

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Analytical solutions of the Klein–Gordon equation with a combined potential

Cited by 33 publications

References 50 publications

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

A study of thermodynamic properties of quadratic exponential-type potential in D-dimensions

Approximate solutions of the Schrödinger equation with energy-dependent screened Coulomb potential in D – dimensions

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