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

TL;DR

This paper solves the DKP equation with a cusp potential for spin-one particles, revealing transmission resonances and bound states, including particle-antiparticle pairs, using analytical solutions involving Whittaker functions.

Contribution

It provides analytical solutions for the DKP equation with a cusp potential, highlighting transmission resonances and bound states for spin-one particles.

Findings

Transmission resonances are present.

Bound states include particle-antiparticle pairs.

Solutions are expressed in terms of Whittaker functions.

Abstract

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.