Pseudospin Symmetry for a Ring-Shaped Non-spherical Harmonic Oscillator Potential

Abstract

The pseudospin symmetry for a ring-shaped non-spherical harmonic oscillator potential is investigated by solving the Dirac equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained, the algebraic property of the energy equation and some particular cases are also discussed.

Application of Nikiforov-Uvarov Method for Non-central Potential System Solution

“…The orbital momentum number and the polar wave function are achieved from (114) by applying (12), (13), (16), (17), (22),…”

“…Three dimensional harmonics oscillator is one of exactly solvable potential that used to describe the nuclei, atomic or molecular vibration. Noncentral potential composed of spherical harmonics oscillator with square of inverse potential together with ring-shaped non-central potential, or double ring shaped potential have been investigated intensively by some authors [22][23][24][25]. The RosenMorse potential is trigonometric potential which was proposed by Rosen-Morse [26] in 1935 and was used to describe the quark-gluon dynamics.…”

Novel bound states treatment of the two dimensional Schrödinger equation with pseudocentral potentials plus multiparameter noncentral potential

“…Recently, much considerable effort for variety forms of NCPs has been expanded on the solutions of Schrödinger, Dirac and Klein-Gordon equations. The Feynman's path integral treatment [26][27][28][29][30] and the Green's function technique [31,32], the (Lie) algebraic/group theoretical approach [33][34][35][36], nonbijective canonical transformation [3,37], supersymmetric (SUSY) quantum mechanical formalism [38][39][40][41][42][43][44][45][46] and the NU-analytic method [47][48][49][50][51][52][53][54][55][56][57][58] as well as the applications for both relativistic [59][60][61][62][63][64][65][66][67][68][69][70][71] and other nonrelativistic…”

Approximate Relativistic Solutions for a New Ring-Shaped Hulthén Potential

“…Berkdemir and Cheng [32] investigated the problem of relativistic motion of a spin-1 / 2 particle in an exactly solvable potential consisting of harmonic oscillator potential plus a novel RS dependent potential. Zhang et al [33][34][35] obtained the complete solutions of the Schrödinger and Dirac equations with a spherically harmonic oscillatory RS potential. Ikhdair 10 and p is a real parameter and its value is taken as 1.…”

“…Berkdemir and Cheng [32] investigated the problem of relativistic motion of a spin-1 / 2 particle in an exactly solvable potential consisting of harmonic oscillator potential plus a novel RS dependent potential. Zhang et al [33][34][35] obtained the complete solutions of the Schrödinger and Dirac equations with a spherically harmonic oscillatory RS potential. Ikhdair and Sever obtained the exact solutions of the D-dimensional Schrödinger equation with RS pseudo-harmonic potential [36], modified Kratzer potential [37] and the D-dimensional KG equation with ring-shaped pseudo-harmonic potential [38].…”