Klein–Gordon Solutions for a Yukawa-like Potential

Abstract

The Klein-Gordon equation for a recently proposed Yukawa-type potential is solved with any orbital quantum number l. In the equally mixed scalar-vector potential fields S(r) = ±V (r), the approximate energy eigenvalues and their wave functions for a particle and anti-particle are obtained by means of the parametric Nikiforov-Uvarov method. The non-relativistic solutions are also investigated. It is found that the present analytical results are in exact agreement with the previous ones.

Path integral treatment of a Klein Gordon particle with generalized inverse Quadratic Yukawa potential

“…Our results in tables 1, 2, 3, 4, and 5 show that the energy increases as the quantum numbers (n, ℓ) increase and retain its credibility when seeing the energy behavior for large quantum states, and we can see that our results are very close to the references [8,11,12,[30][31][32][33][34].…”

“…The energy spectra E n,ℓ that are calculated numerically for various values of the quantum numbers n, ℓ, a, b, c and α are shown in tables 1, 2, 3, 4, and 5. To show the accuracy of our method, we compared our results with the formula method [12,31] in table 2 and 3, the Nikiforov-Uvarov method (NU) [30,34] in table 1 and 5 and the proper quantization rule [33] in table 4. Now, we adjust the α, a, b, and c parameters to find solutions for non-relativistic limits and some special implicit cases in GIQY potential.…”

“…The energy eigenvalues (in fm −1 ) of the GIQY potential in units ÿ = c = 1. We set M = 5.0, α = 0.0015 and a = c = 1.0 and b = 2.0 for comparison with the parametric Nikiforov-Uvarov method [30]. Table 2.…”