Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials

Abstract

The bound state solutions of Dirac equations for a trigonometric Scarf potential with a new tensor potential under spin and pseudospin symmetry limits are investigated using Romanovski polynomials. The proposed new tensor potential is inspired by superpotential form in supersymmetric (SUSY) quantum mechanics. The Dirac equations with trigonometric Scarf potential coupled by a new tensor potential for the pseudospin and spin symmetries reduce to Schrödinger-type equations with a shape invariant potential since the proposed new tensor potential is similar to the superpotential of trigonometric Scarf potential. The relativistic wave functions are exactly obtained in terms of Romanovski polynomials and the relativistic energy equations are also exactly obtained in the approximation scheme of centrifugal term. The new tensor potential removes the degeneracies both for pseudospin and spin symmetries.

Analytic Spin and Pseudospin Solutions to the Dirac Equation for the Manning-Rosen Plus Eckart Potential and Yukawa-Like Tensor Interaction

“…In recent years, a lot of effort has been put into solving these relativistic wave equations for various potentials by using different methods [4,5]. Some researchers have investigated the Dirac equation by using a variety of potentials and different methods, such as the spin symmetry in the antinucleon spectrum and tensor type Coulomb potential with spin-orbit number k in a state of spin symmetry and p-spin symmetry [6],bound states of the Dirac equation with positiondependent mass for the Eckart potential [7], the exact solution of Klein-Gordon with the Poschl-Teller double-ring-shaped Coulomb potential [8],the exact solution of the Dirac equation for the Coulomb potential plus NAD potential by using the Nikorov-Uvarov method [9], the potential Deng-Fan and the Coulomb potential tensor using the asymptotic iteration method (AIM) [10],the potential Poschl-Teller plus the Manning Rosen radial section with the hypergeometry method [11], the solution ofKlein-Gordon equation for Hulthen non-central potential inradial part with Romanovski polynomial [12],and the solution [13], the Scarf potential with the new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials [14],for the q-deformed hyperbolic Poschl-Teller potential and the trigonometric Scarf II noncentral potential by using AIM [15],eigensolutions of the deformed Woods-Saxon potential via AIM [16],approximate solutions of the Klein Gordon equation with an improved Manning Rosen potential in D-dimensions using SUSYQM [17], and eigen spectra of the Dirac equation for a deformed Woods-Saxon potential via the similarity transformation [18].…”

Analysis of Energy and Wave Functions and the Thermodynamics Properties of the 6-Dimensional Schrodinger Equation Under Double Ring-Shape Oscillator (Drso) and Manning-Rosen Potentials Using Susy Qm Method

“…For instance, this method has been used to investigate Dirac Equation with Morse potential with tensor interaction (Alsadi, 2015), and Klein Gordon Equation with exponential scalar and vector potential (Ikhdair and Falaye, 2013), relativistic and nonrelativistic wave equation under Poschl-Teller potential and its thermodynamic properties (Taşkın, et al, 2008). Romanovski polynomial method has been used to investigate a quantum mechanical system of Dirac with the effect of Scarf plus new tensor coupling potential (Suparmi, et al, 2014). The quantization rule approach has been used to solve the Schrodinger Equations problem with hyperbolic plus second Poschl-Teller potential (Dong and Gonzalez-Cisneros, 2008).…”

Bound state solutions of a Dirac particle undergoing a tensor interaction potentials via asymptotic iteration method

“…The eigenvalues and egienfunctions of the problem have been investigated by relativistic shape invariant approach [22]. The second one is the trigonometric Scarf tensor potential which has been solved by Romanovski polynomials method [23] and by shape invariance approach [22]. The third potential is Morse-Rosen II which is a well-known interaction potential which has been used to probe the vibrations in diatomic molecules [18].…”