Perturbed Coulomb potentials in the Klein-Gordon equation via the shifted-lexpansion technique

Abstract

A shifted -l expansion technique is introduced to calculate the energy eigenvalues for Klein -Gordon (KG) equation with Lorentz vector and/or Lorentz scalar potentials. Although it applies to any spherically symmetric potential, those that include Coulomb -like terms are only considered. Exact eigenvalues for a Lorentz vector or a Lorentz scalar, and an equally mixed Lorentz vector and Lorentz scalar Coulombic potentials are reproduced. Highly accurate and rapidly converging ground -state energies for Lorentz vector Coulomb with a Lorentz vector or a Lorentz scalar linear potential, V (r) = −A 1 /r + kr, and V (r) = −A 1 /r and S(r) = kr, respectively, are obtained. Moreover, a simple straightforward closed -form solution for a KGparticle in Coulombic Lorentz vector and Lorentz scalar potentials is presented in appendix A.

Anharmonic oscillators energies via artificial perturbation method

“…Herein, it should be noted that Q is a constant that scales the potential V (q) at large -l limit and is set, for any specific choice of l and n r , equal tol 2 at the end of the calculations [11,16]. And, β is to be determined in the sequel.…”

“…Up to this point, one would conclude that the above procedure is nothing but an imitation of the eminent shifted large-N expansion (SLNT) [12,14,16,[20][21][22]. However, because of the limited capability of SLNT in handling largeorder corrections via the standard Rayleigh-Schrödinger perturbation theory, only low-order corrections have been reported, sacrificing in effect its preciseness.…”

“…One has therefore to sum up such series [7][8][9][10]. Hence, apparently artificial perturbation recipes have been devised and shown to be ways to make progress [2,3,[11][12][13][14][15][16]. Without being exhaustive, several eligible methods have been used to calculate the eigenvalues and eigenfunctions for…”

Fermionic particles with position-dependent mass in the presence of inversely quadratic Yukawa potential and tensor interaction

“…To normalize the wave functions, some of the special procedures for the beta function is given in the following form [32][33][34][35][36][37][38]:…”

Dirac and Klein Gordon particles in complex Coulombic fields: a similarity transformation

“…• (14) reduces to Klein-Gordon [23] with complex Coulomb-like Lorentz scalar and Lorentz vector potentials, S(r) = −i A 2 /r and V (r) = −i A 1 /r, respectively. That is…”