Exact solution of the Dirac–Eckart problem with spin and pseudospin symmetry

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

“…Recently, the study of exponential-type potentials has attracted much attention from many authors (for example, cf, ). These physical potentials include the Woods-Saxon [7,8], Hulthén [9][10][11][12][13][14][15][16][17][18][19][20][21][22], modified hyperbolic-type [23], ManningRosen [24][25][26][27][28][29][30][31], the Eckart [32][33][34][35][36][37], the Pöschl-Teller [38] and the Rosen-Morse [39,40] potentials.…”

“…The bound state solutions of the s-wave Klein-Gordon (KG) equation with equally mixed Rosen-Morse-type (Eckart and Rosen--Morse well) potentials have been studied [52]. The bound state solutions of the s-wave Dirac equation with equal vector and scalar Eckart-type potentials in terms of the basic concepts of the shape-invariance approach in the SUSYQM have also been studied [34][35][36][37]. The spin symmetry and pseudospin symmetry in the relativistic Eckart potential have been investigated by solving the Dirac equation for mixed potentials [38].…”

“…Unfortunately, the wave equations for the Eckart-type potential can only be solved analytically for zero angular momentum states because of the centrifugal potential term. Some authors [32][33][34][35][36][37][38] studied the analytical approximations to the bound state solutions of the Schrödinger equation with Eckart potential by using the usual existing approximation scheme proposed by Greene and Aldrich [53] for the centrifugal potential term. This approximation has also been used to study analytically the arbitrary l -wave scattering state solutions of the Schrödinger equation for the Eckart potential [54,55].…”

Dynamical symmetries of the Klein–Gordon equation

“…Recently, many works about the Dirac or the Klein-Gordon (KG) equation with scalar and vector potentials of equal magnitude (SVPEM) are reported [1,2,3,4,5,6,7,8,9,10,11,12] .When the potentials are spherical, the Dirac equation is said to have the spin or pseudospin symmetry corresponding to the same or opposite sign. These symmetries, which have been observed in the hadron and nuclear spectroscopies for a long time [13,14], are derived from the investigation of the dynamics between a quark and an antiquark [15,16].…”

Solution of Klein Gordon Equation for Some Diatomic Molecules with New Generalized Morse-like Potential Using SUSYQM

“…These techniques include asymptotic iteration method (AIM), 9 the Nikiforov-Uvarov method (NU), 10 supersymmetric quantum mechanices, 11 and others. Amongst the potentials studied with these techniques are the Manning-Rosen Potential, 12, 13 Hulthen Potential, 14,15 Eckarttype Potential, 16,17 Wood-Saxon Potential, 18,19 Poschl-Teller Potential. 20 Many contributions from different authors shows that the analytical solution of KGE are possible only in the swave case (l = 0) while for , it is solved by using suitable approximation scheme.…”