Dirac particles in the presence of the Yukawa potential plus a tensor interaction in SUSYQM framework

Abstract

Applying an appropriate approximation scheme to deal with the centrifugal term, pseudospin and spin symmetric solutions of the Dirac–Yukawa problem with tensor interaction are investigated based on supersymmetric quantum mechanics (SUSYQM) and shape invariance (SI) formalism. We show that the energy eigenvalues equation is simply obtained by using the methodology of SUSYQM and SI. The corresponding wave functions are obtained in terms of hypergeometric functions. Effects of tensor interaction on the bound states and eigenfunctions are also investigated numerically. Further, we compare our results with those given in the literature, which are obtained by using the Nikiforov–Uvarov and asymptotic iteration methods.

Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach

“…The reason is that most of the exponential-type potentials play an important role in physics, e.g. Yukawa potential is used in plasma, solid-state and atomic physics [1]. As a result, many authors have solved both relativistic and non-relativistic wave equations with these potentials.…”

“…Hamzavi et al [8] obtained approximate spin and pseudospin solutions of the Dirac equation for inversely quadratic Yukawa potential and tensor interaction. Maghsoodi et al [1] solved Dirac particles in the presence of Yukawa potential plus a tensor interaction in SUSY QM frame work. Ikhdair [9] obtained on the bound state solutions of the Manning-Rosen potential including an improved approximation to the orbital centrifugal term.…”

κ state solutions for the fermionic massive spin-½ particles interacting with double ring-shaped Kratzer and oscillator potentials

“…Furthermore, some authors have investigated the spin symmetry and Pseudospin symmetry under the Dirac equation in the presence and absence of coulomb tensor interaction for some typical potentials such as the Harmonic oscillator potential [16][17][18][19][20][21][22][23][24][25], Coulomb potential [26,27], Woods-Saxon potential [28,29], Morse potential [30][31][32][33][34][35], Eckart potential [36,37], ring-shaped non-spherical harmonic oscillator [38], Pöschl-Teller potential [39][40][41][42][43], three parameter potential function as a diatomic molecule model [44], Yukawa potential [45][46][47][48][49], pseudoharmonic potential [50], Davidson potential [51], Mie-type potential [52], Deng-Fan potential [53], hyperbolic potential [54] and Tietz potential [55].…”

Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential

“…Recently, the asymptotic iteration method (AIM) [15][16][17] an elegant, efficient technique to solve second-order homogeneous differential equations, has been the subject of extensive investigation in recent years, particularly when dealing withe non central potential. The Schrödinger equation has been investigated for several potentials as the Woods-Saxon potential [18][19][20], harmonic oscillator potential [21], Hulthén potential [22][23][24][25], Kratzer potential [26], generalized q-deformed Morse potential [27], modifed Woods-Saxon potential [28], Makarov potential [29], deformed Woods-Saxon Potential [30], Pseudoharmonic potential [31,32], Yukawa potential [33,34] and Eckart potential [35,36]. Very recently, the Schrödinger equation in generalized D dimensions for different potentials is getting more attention with the aim of generalizing the solutions to multidimensional space for many potentials [37][38][39][40][41][42][43][44][45][46].…”