The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

Abstract

Abstract:The approximately analytical bound and scattering state solutions of the arbitrary −wave Klein-Gordon equation for the mixed Manning-Rosen potentials are carried out by an improved new approximation to the centrifugal term. The normalized analytical radial wave functions of the −wave Klein-Gordon equation with the mixed Manning-Rosen potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states, reduce to the bound states of those at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and the special case for −wave is studied briefly.PACS (2008)

Arbitrary ℓ-state solutions of the Klein-Gordon equation with the Manning-Rosen plus a Class of Yukawa potentials

“…Among them, the NU and SUSYQM methods have received great interest. By using these two techniques, many works have been conducted to obtain either exact or approximate solutions of the KG equation with some well-known potentials as follows: Manning-Rosen Potential [23,24,25], Yukawa potential [26,27,28], Hulthen Potential [29,30,31], generalized Hulthen potential [32,33,34], Kratzer Potential [35], Wood-Saxon Potential [36,37,38] and Deng-Fan molecular potentials [39]. Similarly for the case of combined potentials: ManningRosen plus Hulthn potential [40], Hulthn plus a Ring-Shaped like potential [41], Hulthn plus Yukawa potential [42] and references in there [43].…”

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

“…Taking 1,   their approximation can be reduced to the usual approximation [9,19]. Quite recently, we have also proposed a new approximation scheme for the centrifugal term [13,14]. The Nikiforov-Uvarov (NU) method [60] and other methods have also been used to solve the D-dimensional Schrödinger equation [61] and relativistic D-dimensional KG equation [62], Dirac equation [6,15,39,40,63] and spinless Salpeter equation [64].…”

“…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.…”

Non-relativistic continuous states in arbitrary dimension for a ring-shaped pseudo-Coulomb and energy-dependent potentials

“…Therefore, scattering problem has become an interesting topic in relativistic/non-relativistic quantum mechanics, and scattering of a non-relativistic particle by a potential can be treated exactly by finding the continuum solutions of the Schrödinger equation. Recently, there has been continuous interest in studying the solutions continuous states within the framework of non-relativistic and relativistic quantum mechanics for central and non-central potentials [7][8][9][10][11][12][13][14][15][16][17].…”