Approximate analytical solutions of the relativistic equations with the Deng–Fan molecular potential including a Pekeris-type approximation to the (pseudo or) centrifugal term

Abstract

By employing the Pekeris-type (or a new improved approximation) to deal with the (pseudo or) centrifugal term, we solve the Klein–Gordon and Dirac equations with equally mixed scalar and vector Deng–Fan molecular potentials for all values of l (orbital the angular momentum quantum number) and κ (spin–orbit coupling quantum number), respectively. Using the formalism of the Nikiforov–Uvarov method, the approximate analytical bound state energy equations and the associated two-component spinors corresponding to the two relativistic equations are obtained. Also, special cases including the non-relativistic limits of the relativistic equation are obtained.

Solutions of the Dirac Equation With the Shifted Deng–fan Potential Including Yukawa-Like Tensor Interaction

“…where σ(z) and σ(z) are polynomials, at most second degree, and τ (z) is a polynomial of first degree [31,39,40,51,57,73,74,93,98,99,102,104,103,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122].…”

“…This potential has been widely studied by some researchers in various applications [65,66,67,68,69,70,71,72,73,74,75]. This potential model can be used to describe the motion of the nucleons in the mean field produced by the interactions between nuclei [65].…”

Molecular Spinless Energies of the Modified Rosen-Morse Potential Energy Model

“…27 The Pekeris approximation approach has been widely used to investigate the analytical solutions of the Klein-Gordon equation with various molecular potential models. [11][12][13] We replace the centrifugal potential energy term by the following form…”

Exact Bound State Solution of Qdeformed Woods-Saxon Plus Modified Coulomb Potential Using Conventional NIKIFOROV-UVAROV Method

“…Schrodinger equation forms the non-relativistic part of the quantum mechanics and obtaining both exact and arbitrary solution with some chosen potentials has been of great interest because of its enormous applications [1][2] Obtaining the total wave function and its corresponding eigen value is essential and very important as its provides the necessary information for the quantum mechanical systems [3][4][5]. Many authors have provided both exact and approximate solutions to Schrodinger equation using different solvable potentials such as Pseudoharmonic, Rosen-Morse, coulomb , Yukawa, Kratzer ,Hellmann potentials [6][7][8][9].…”