Spinless particles in the field of unequal scalar—vector Yukawa potentials

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 l-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 the 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 the energy states of the KG—Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2–6.