An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry

Abstract

By using an improved approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation for the generalized Morse potential with arbitrary spin-orbit quantum number κ. In the presence of spin and pseudospin symmetry, the analytic bound state energy eigenvalues and the associated upper-and lower-spinor components of two Dirac particles are found by using the basic concepts of the Nikiforov-Uvarov method. We study the special cases when κ = ±1 (l = l = 0, s-wave), the non-relativistic limit and the limit when α becomes zero (Kratzer potential model). The present solutions are compared with those obtained by other methods.

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

“…However, analytical solutions are possible only in a few simple cases such as the hydrogen atom and the harmonic oscillator [1,2]. Most quantum systems could be solved only by using approximation schemes like rotating Morse potential via Pekeris approximation [3][4][5] and the generalized Morse potential by means of an improved approximation scheme [6]. Recently, the study of exponential-type potentials has attracted much attention from many authors (for example, cf, ).…”

“…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].…”

Approximate analytical solutions to relativistic and nonrelativistic Pöschl–Teller potential with its thermodynamic properties

“…Using Dirac wave equation and Dirac spinor wave functions, the two-coupled second-order ordinary differential equations for the upper and lower components of the Dirac wave function can be obtained as [34,35,53,54,55,56] …”

Energy States of Some Diatomaic Molecules: The Exact Quantisation Rule Approach

“…Because of its importance in chemical physics, molecular spectroscopy, molecular physics and related areas, the bound state solutions of the relativistic and non-relativistic wave equations have been studied by several authors [7,29,46,47]. The shape of this potential with respect to some diatomic molecules is shown in figure1.…”

“…This is done in an attempt to finding a more suitable diatomic potential to describe the vibrational spectrum, qualitatively similar to the Morse potential with the correct asymptotic behaviour as the inter-nuclear distance approaches zero. This potential model can be used to describe the motion of the nucleons in the mean field produced by the interactions between nuclei [47]. This potential has been used to describe diatomic molecular energy spectra and electromagnetic transitions and it is an ideal inter-nuclear potential in diatomic molecules with the same behavior for r → 0.…”