Spinless particles in the field of unequal Scalar-Vector Yukawa potentials

TL;DR

This paper derives analytical and numerical solutions for spin-zero Klein-Gordon particles in unequal scalar-vector Yukawa potentials, revealing inter-dimensional degeneracies and the impact of spatial dimensions on energy levels.

Contribution

It introduces a combined analytical and numerical approach to solve the Klein-Gordon equation with Yukawa potentials, including an approximation scheme and validation via the amplitude phase method.

Findings

Analytical energy eigenvalues and wave functions obtained using the NU method.

Numerical energy levels verified with the amplitude phase method.

Inter-dimensional degeneracy observed among energy states.

Abstract

We present analytical bound state solutions of the spin-zero Klein-Gordon (KG) particles in the field of unequal mixture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary -state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov-Uvarov (NU) method. Further, we solve the KG-Yukawa problem for its exact numerical energy eigenvalues via amplitude phase (AP) method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst energy states of the KG-Yukawa problem. The dependence of the energy on the dimension is numerically discussed for spatial dimensions