The DKP Equation in Presence of a Cusp Potential: Transmission Resonances and Bound States

In this article, we solve the Duffin–Kemmer–Petiau (DKP) equation in the presence of the cusp potential for spin–one particles. We derived the scattering solutions and calculated the bound states in terms of the Whittaker functions. We show that transmission resonances are present, as well as the particle–anti-particle bound states.