Solutions of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math>-Dimensional Schrödinger Equation with the Hyperbolic Pöschl-Teller Potential plus Modified Ring-Shaped Term

Assi, I. A.; Ikot, Akpan N.; Chukwuocha, Ephraim O.

doi:10.1155/2018/4536543

Cited by 10 publications

(3 citation statements)

References 39 publications

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“…In a spherical potential model Vtrue(rtrue), the time independent Schrödinger equation is given by [28, 29, 30, 31, 32, 33]. true[−ℏ2∇22μ+Vtrue(rtrue)true]ψnℓmtrue(r,θ,ϕtrue)=Enkψnℓmtrue(r,θ,ϕtrue),where ℓ and n are orbital angular momentum and radial quantum number respectively, ψnℓmtrue(r,θ,ϕtrue) is the wave function, μ and ℏ are reduced mass and Planck constant respectively, r is the internuclear separation and Enℓ is the non-relativistic energy.…”

Section: Theory/calculationmentioning

confidence: 99%

Approximate eigensolutions of the attractive potential via parametric Nikiforov-Uvarov method

Onate

Adebimpe

Lukman

et al. 2018

Heliyon

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The approximate analytical solutions of the non-relativistic Schrӧdinger equation for the Attractive potential model with the centrifugal term are investigated using the elegant methodology of the parametric Nikiforov-Uvarov. The energy equation and the corresponding un-normalized radial wave functions are obtained in a close and compact form after a proper Greene-Aldrich approximation scheme is applied. By changing the numerical values of some potential strengths, special cases of the Attractive potential are investigated in detail. The effects of the potential strengths and potential range respectively on the energy are also studied. The energy is found to be very sensitive to each of the potential parameters. Some theoretic quantities such as information energy, Rẻnyi entropy and Tsallis entropy.

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Section: Theory/calculationmentioning

confidence: 99%

Approximate eigensolutions of the attractive potential via parametric Nikiforov-Uvarov method

Onate

Adebimpe

Lukman

et al. 2018

Heliyon

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“…Various approaches have been used to study the Dirac wave equation. Using the Nikiforov-Uvarov method [11][12][13] and supersymmetric quantum mechanics approach [6,14,15], Chen [16] found pseudospin symmetric solutions of the Dirac equation with the modified Rosen-Morse potential. Studies of the Dirac equation have been conducted using the Feynman path integral method [17][18][19] and the asymptotic iteration method [20,21].…”

Section: Introductionmentioning

confidence: 99%

Study of energies spectra and thermodynamic properties of the relativistic Dirac equation using Feynman path integral method

2023

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In the current paper the contribution of a Coulomb-like potential tensor interaction on the solution of the Dirac equation with a new generalized Morse-like potential is investigated using Feynman path integral method. Relativistic and non-relativistic energy spectra were obtained. Using the resulting non-relativistic energy eigen equations, three diatomic molecules (H2, LiH, and HCl) were investigated and their thermodynamic properties, including mean energy, free energy, entropy, and speciﬁc heat capacity were obtained. A comparison with the available literature shows that the thermodynamic plots obtained match those in the literature.

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“…Further generalizing the hyperbolic Pöschl-Teller potential is undoubtedly essential. In recent years, many scholars have made extensive studies on the hyperbolic potential from different perspectives [12][13][14]. Although they have studied based on SUSYQM, they only give a form of shape invariance.…”

Section: Introductionmentioning

confidence: 99%

Shape Invariance of Solvable Schrödinger Equations with the Generalized Hyperbolic Pöschl-Teller Potential

Zhong

et al. 2022

Advances in Mathematical Physics

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In atomic and molecular physics, the Pöschl-Teller potential and its modified form (hyperbolic Pöschl-Teller potential) are particularly significant potentials. It is of great importance to study the Schrödinger equation with those potentials. In this paper, we further extend the hyperbolic Pöschl-Teller potential through generalizing the superpotential of that potential of the form Atanh (αx)-Bcoth (αx) to the more general form -Atanh (npx)-Bcoth (mpx). First, we introduce briefly the shape invariance and the potential algebra in supersymmetric quantum mechanics. Second, we derive three additive shape invariances, which are related to parameters A and B of the partner potentials with the generalized superpotential, and discuss the eigenfunctions and eigenvalues in detail. Although the superpotential has two parameters, those shape invariances still belong to the one-parameter form. The reason is that there is always a constraint relationship between A and B in the additive shape invariance of the partner potentials. Third, through the potential algebra approach, we obtain the relevant shape invariance and calculate the corresponding eigenvalue of the Schrödinger equation with the potential of the generalized superpotential. The calculation shows that the algebraic form shape invariance of the partner potentials with that superpotential is anastomotic to the above. Last, we make a summary and outlook.

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Solutions of the D-Dimensional Schrödinger Equation with the Hyperbolic Pöschl-Teller Potential plus Modified Ring-Shaped Term

Cited by 10 publications

References 39 publications

Approximate eigensolutions of the attractive potential via parametric Nikiforov-Uvarov method

Approximate eigensolutions of the attractive potential via parametric Nikiforov-Uvarov method

Study of energies spectra and thermodynamic properties of the relativistic Dirac equation using Feynman path integral method

Shape Invariance of Solvable Schrödinger Equations with the Generalized Hyperbolic Pöschl-Teller Potential

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