Bound-state solutions of the modified Klein–Gordon and Schrödinger equations for arbitrary l-state with the modified Morse potential in the symmetries of noncommutative quantum mechanics

Abstract

In this work, approximate analytical solutions of both modi(cid:28)ed Klein(cid:21)Gordon equation and Schr(cid:4)odinger equation in noncommutative relativistic and nonrelativistic three-dimensional real space have been explored by using the Pekeris approximation scheme to deal with the centrifugal term, Bopp’s shift method and standard perturbation theory. We present the bound-state energy equation with a newly proposed potential called the modi(cid:28)ed Morse potential under the condition of equal scalar and vector potentials. The potential is a superposition of the Morse potential and some exponential radial terms. The aim of combining these potentials is to have an extensive application. We show that the new energy depends on the global parameters ( Θ c and σ c ) characterizing the noncommutativity space-space and the potential parameter ( D e , r e , α ) in addition to the Gamma function and the discreet atomic quantum numbers ( j, l, s, m ) . The present results are applied in calculating both the energy spectrum for a few heterogeneous (LiH, HCl, NO) and homogeneous (H 2 , I 2 , O 2 ) diatomic molecules. We have also discussed some special cases of physical importance.