Manning-Rosen Potential Research Articles

Approximate arbitrary κ-state solutions of Dirac equation with Schiöberg and Manning-Rosen potentials within the coulomb-like Yukawa-like and generalized tensor interactions

The effects of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT) and generalized tensor (GLT) interactions are investigated in the Dirac theory with Schioberg and Manning-Rosen potentials within the framework of spin and pseudospin symmetries using the Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions have been approximately obtained in the case of spin and pseudospin symmetries. We have also reported some numerical results and figures to show the effects these tensor interactions.

Generation of exactly solvable potentials of the D-dimensional position-dependent mass Schrödinger equation using the transformation method

We apply the extended transformation method to the constant-mass radial Schrodinger equation satisfied by a radially symmetric central potential in order to obtain exactly solvable quantum systems with a position-dependent mass in a space of arbitrary dimension in the nonrelativistic limit. The method consists of a coordinate transformation, a subsequent functional transformation, and a set of ansatzes for the mass function leading to the appearance of exactly solvable quantum systems with position-dependent masses. We also show that the Zhu-Kroemer ordering for the fitting parameter values is natural for systems with a radially symmetric mass function and a central potential. As an example, we apply the method to the Manning-Rosen potential and to the Morse potential with different choices of the mass functions. We also indicate an application of the method to the Hulthen potential.

Spin and Pseudospin Symmetry in Generalized Manning-Rosen Potential

Spin and pseudospin symmetric Dirac spinors and energy relations are obtained by solving the Dirac equation with centrifugal term for a new suggested generalized Manning-Rosen potential which includes the potentials describing the nuclear and molecular structures. To solve the Dirac equation the Nikiforov-Uvarov method is used and also applied the Pekeris approximation to the centrifugal term. Energy eigenvalues for bound states are found numerically in the case of spin and pseudospin symmetry. Besides, the data attained in the present study are compared with the results obtained in the previous studies and it is seen that our data are consistent with the earlier ones.

Scattering phase shifts of Dirac equation with Manning-Rosen potential and Yukawa tensor interaction

Bound-state solutions of the Dirac equation with Yukawa tensor interaction and Manning-Rosen potential are obtained for any arbitrary state. The energy eigenvalues and the corresponding eigenfunctions are obtained using the parametric Nikiforov–Uvarov method. Thereby, the radial wavefunctions of scattering states are obtained in terms of hypergeometric functions. Next, using the basic properties of the hypergeometric function, the phase-shifts are reported. In addition, some numerical results are included in the case of pseudospin and spin symmetry limits.

Approximate solutions of Klein—Gordon equation with improved Manning—Rosen potential in D-dimensions using SUSYQM

In this paper, we present solutions of the Klein-Gordon equation for the improved Manning—Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energy levels and the corresponding wave functions expressed in terms of Jacobi polynomial in a closed form for arbitrary l state. We also calculate the oscillator strength for the potential.

Approximate solutions of Dirac equation for Tietz and general Manning-Rosen potentials using SUSYQM

In this paper, we consider the relativistic Dirac equation with Tietz and general Manning-Rosen potential. By using appropriate approximation, we obtained the approximate analytical solutions of the Dirac equation for the combined potential via the supersymmetric quantum mechanics (SUSYQM). Within the framework of spin and pseudospin symmetry limits, we obtained the relativistic energy eigenvalus and the corresponding components of the wave functions for Tietz and Manning-Rosen potential using the SUSYQM. We have also reported some numerical results and figures to show the effect of the tensor interactions.

Relationship of the Williams-Poulios and Manning-Rosen Potential Energy Models for Diatomic Molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved form of the Williams-Poulios potential energy model. It is found that the negative Williams-Poulios potential model is equivalent to the Manning-Rosen potential model for diatomic molecules. We observe that the Manning-Rosen potential is superior to the Morse potential in reproducing the interaction potential energy curves for the \({{a}^{3} \Sigma_{{\rm u}}^{+}}\) state of the 6Li2 molecule and the \({{X}^{1} \sum^{+}}\) state of the SiF+ molecule.

Spin-one Duffin–Kemmer–Petiau equation in the presence of Manning–Rosen potential plus a ring-shaped-like potential

We present the solution of the Duffin–Kemmer–Petiau equation for Manning–Rosen potential plus a ring-shaped-like potential in (1+3)-dimensional space–time for spin-one particles within the framework of an exponential approximation for the centrifugal term. We have used the Nikiforov–Uvarov method in our calculations. The radial wavefunction and the angular wavefunctions are expressed in terms of Jacobi polynomials. We have also represented some numerical results for the Manning–Rosen potential plus a ring-shaped-like potential.

Studies on bound-state spectra of Manning–Rosen potential

Accurate ro-vibrational energies, eigenfunctions, radial densities, expectation values are presented for the exponential-type Manning–Rosen (MR) potential. Bound states, accurate up to ten significant figure are obtained by employing a simple, reliable generalized pseudospectral (GPS) method. All 55 eigenstates with n ≤10 are treated for arbitrary values of potential parameters, covering a wide range of interaction, through a non-uniform, optimal spatial radial discretization. A detailed investigation has been made on energy changes with respect to screening and other potential parameters. A systematic estimation of critical screening parameters is given for these eigenstates. Special emphasis has been given to higher states and in the vicinity of critical screening region. A thorough comparison with literature results is made wherever possible. This surpasses the accuracy of all other existing methods currently available. Several new states are reported for the first time. In short, a simple, efficient scheme for accurate calculation of this and other molecular potentials is offered.

ℓ-State Solutions of Multiparameter Exponential-type Potentials

In the present work, bound state solutions for a class of multiparameter exponential-type potential are obtained in the frame of the Greene and Aldrich approximation for the centrifugal term. The proposal is general and their usefulness is exemplified with the treatment of the Eckart, Manning-Rosen, Hulthen and Deng Fan potentials that are obtained straightforwardly without resorting to specialized methods of solution for each specific potential, as usually is done. Furthermore, the proposal admits other approximations for the centrifugal term indicating an improvement to procedures developed with the same objective. So, our proposal can be considered as an unified treatment of the ℓ-state solutions for exponential-type potentials and can be used to find new solvable potentials.

Generalized tensor interaction and relativistic spin and pseudospin symmetries with the Manning-Rosen potential

We have investigated the Manning-Rosen potential under the framework of spin and pseudospin symmetries with generalized tensor interaction (GTI) using the parametric generalization of Nikiforov-Uvarovmethod. We have obtained the energy eigenvalues and the corresponding eigenfunction. We have also reported some numerical results and figures to show the effect of tensor interaction. The role of GTI is investigated in details. It is seen that the degenerate doublets in spin and pseudospin are changed due to the presence of GTI.

Generalized Tensor Interaction and Relativistic Spin and Pseudospin Symmetries with the Manning–Rosen Potential

Generalized Tensor Interaction and Relativistic Spin and Pseudospin Symmetries with the Manning–Rosen Potential

Hulthén and Coulomb-Like Potentials as a Tensor Interaction within the Relativistic Symmetries of the Manning-Rosen Potential

The bound-state solutions of the Dirac equation for the Manning-Rosen potential are presented approximately for arbitrary spin-orbit quantum numberκwith the Hulthén and Coulomb-like potentials as a tensor interaction. The generalized parametric Nikiforov-Uvarov (NU) method is used to obtain energy eigenvalues and corresponding two-component spinors of the two Dirac particles and these are obtained in the closed form by using the framework of the spin symmetry and p-spin symmetry concept. We have also shown that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.

The Scattering and Bound States of the Schrödinger Particle in Generalized Asymmetric Manning-Rosen Type Potential

We solve exactly one-dimensional Schrödinger equation for the generalized asymmetric Manning-Rosen (GAMAR) type potential containing the different types of physical potential that have many application fields in the nonrelativistic quantum mechanics and obtain the solutions in terms of the Gauss hypergeometric functions. Then we determine the solutions for scattering and bound states. By using these states we calculate the reflection and transmission coefficients for scattering states and achieve a correlation that gives the energy eigenvalues for the bound states. In addition to these, we show how the transmission and reflection coefficients depend on the parameters which describe shape of the GAMAR type potential and compare our results with the results obtained in earlier studies.

Hyperbolic Manning-Rosen potential under spin and pseudospin symmetries of the Dirac equation with Coulomb-Hulthén-like tensor interactions

Hyperbolic Manning-Rosen potential under spin and pseudospin symmetries of the Dirac equation with Coulomb-Hulthén-like tensor interactions

On the equivalence of the Badawi–Bessis–Bessis, Wei and Tietz potential energy functions for diatomic molecules

It is found that the general potential energy expression introduced by Badawi et al for several empirical potential energy functions that is conventionally defined in terms of five parameters, actually only has four independent parameters. It is demonstrated exactly that the Badawi–Bessis–Bessis potential is equivalent to the well-known Tietz potential model for diatomic molecules. When parameter a in the Badawi–Bessis–Bessis potential function has the values 0, +1 and −1, the Badawi–Bessis–Bessis potential becomes the standard Morse, Rosen–Morse and Manning–Rosen potentials, respectively.

ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE MANNING–ROSEN POTENTIAL PLUS A RING-SHAPED-LIKE POTENTIAL

The analytical solution of the Schrödinger equation for the Manning–Rosen potential plus a ring-shaped-like potential is obtained by applying the Nikiforov–Uvarov method by using the improved approximation scheme to the centrifugal potential for arbitrary l states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states.

Pekeris approximation – another perspective

Abstract Inspired on the Pekeris approximation for the centrifugal term, we elaborate a method of resolution for the Schrodinger equation subject to a potential V ( r ) of a form more general than the exponential one. Generalizing the Pekeris approximation, we solve the Schrodinger equation with Rosen–Morse and Manning–Rosen potentials including the centrifugal term. The bound state energy eigenvalues for these potentials and for arbitrary values of n and l quantum numbers are presented.

Dirac equation under Manning-Rosen potential and Hulthén tensor interaction

We study the Dirac equation with scalar and vector Manning-Rosen potentials and a Hulthen tensor term in the pseudospin and spin symmetry limits. The energy eigenvalues and the corresponding upper- and lower-spinor wave functions are obtained using the Nikiforov-Uvarov (NU) method and proper approximations for any spin-orbit coupling term κ. Some numerical results of the energy eigenvalues equations and the upper- and lower-spinor wave functions are included to reveal the effect of the tensor interaction on the system.

Calculation of the interaction potential energy curve and vibrational levels for the state of molecule

Abstract We solve the Schrodinger equation with the improved expression of the Manning–Rosen empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curve for the a 3 Σ u + state of Li 2 7 molecule is modeled by employing Manning–Rosen potential model. Favorable agreement for the Manning–Rosen potential is found in comparing with ab initio data. The vibrational energy levels predicted by using the Manning–Rosen potential for the a 3 Σ u + state of Li 2 7 are in good agreement with the RKR data and ab initio determinations.