Transmission resonances in the Duffin–Kemmer–Petiau equation in (1+1) dimensions for an asymmetric cusp potential

The dynamics of the spin-1 particle is studied using the Duffin–Kemmer–Petiau (DKP) equation. In this study, we exactly solve the one-space-dimensional DKP equation for the general form of a cusp potential. We obtain bound and scattering states and, using these solutions, investigate the condition for the existence of supercriticality and transmission resonances. In contrast to the results suggested in previous studies for a spin-1/2 particle moving in a same-type cusp potential, the results presented here demonstrate that the transmission resonance phenomenon for a spin-1 particle occurs not only for the symmetric but also for the asymmetric form of the cusp potential. The dependence of the transmission coefficient on the potential shape parameters and potential barrier strength is also analyzed.