The DKP equation with position-dependent mass under smooth barrier potential

In this work, we study the DKP equation in the presence of smooth barrier potential with PDM in space–time (1+1) dimensions. The eigenfunctions are determined in terms of the confluent Heun function [Formula: see text]. The transmission and reflection coefficients are calculated, and special cases as rectangular barrier and step potential are analyzed. A numerical study is presented for the transmission and reflection coefficients graphs for some values of the parameters [Formula: see text] are plotted.