Akpan N. Ikot

APPROXIMATE RELATIVISTIC κ-STATE SOLUTIONS TO THE DIRAC-HYPERBOLIC PROBLEM WITH GENERALIZED TENSOR INTERACTIONS

In this paper, we present the approximate analytical solutions of the Dirac equation for hyperbolical potential within the frame work of spin and pseudospin symmetries limit including the newly proposed generalized tensor interaction (GTI) using the Nikiforov–Uvarov (NU) technique. We obtained the energy eigenvalues and the corresponding eigenfunction using the generalized parametric NU method. The numerical results of our work reveal that the presence of the GTI changes the degeneracy between the spin and pseudospin state doublets.

Scattering State of Klein-Gordon Particles by q -Parameter Hyperbolic Poschl-Teller Potential

The one-dimensional Klein-Gordon equation for equal vector and scalar -parameter hyperbolic Poschl-Teller potential is solved in terms of the hypergeometric functions. We calculate in detail the solutions of the scattering and bound states. By virtue of the conditions of equation of continuity of the wave functions, we obtained explicit expressions for the reflection and transmission coefficients and energy equation for the bound state solutions.

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.

Klein-Gordon equation particles in exponential-type molecule potentials and their thermodynamic properties in D dimensions

Abstract.In this paper we use the Nikiforov-Uvarov method to obtain the approximate solutions for the Klein-Gordon equation with the deformed five-parameter exponential-type potential (DFPEP) model. We also obtain solutions for the Schrödinger equation in the presence of DFPEP in non-relativistic limits. In addition, we calculate in the non-relativistic limits thermodynamics properties, such as vibrational mean energy U, free energy F and the specific heat capacity C. Special cases of the potential are also discussed.

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

We study the d-dimensional Schrodinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov—Uvarov method. We obtain energy eigenvalues and the corresponding wave function expressed in terms of a Jacobi polynomial. We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen—Morse potential in three dimensions. Numerical results are also computed for the energy spectrum and the potentials.

Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formalism of the Dirac equation with a generalized Hylleraas potential of the form V(r) = V0(a + exp (λr))/(b + exp (λr)) + V1(d + exp (λr))/(b + exp (λr)). We obtain the bound state energy eigenvalue and the corresponding eigenfunction expressed in terms of the Jacobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.

Exact Solutions of Schrodinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ2/2Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2 and its exact solutions are presented via the Nikiforov–Uvarov method. The angle dependent part V(θ) = (ħ2 / 2 Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2, which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov{Uvarov Method

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov–Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseudospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.

Relativistic symmetries of Deng—Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interactions

Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combination of Deng—Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are considered. The energy equation is obtained by using the Nikiforov—Uvarov method and the corresponding wave functions are expressed in terms of the hypergeometric functions. The effects of the Coulomb and Yukawa tensor interactions are numerically discussed as well.

Bound-State Solutions of the Klein-Gordon Equation with -Deformed Equal Scalar and Vector Eckart Potential Using a Newly Improved Approximation Scheme

We present the analytical solutions of the Klein-Gordon equation for q-deformed equal vector and scalar Eckart potential for arbitrary -state. We obtain the energy spectrum and the corresponding unnormalized wave function expressed in terms of the Jacobi polynomial. We also discussed the special cases of the potential.