Investigation of the wave equation for one Dirac and one Duffin-Kemmerparticle : a new form of the Klein paradox

Abstract

The wave equation for one Dirac and one Duffin-Kemmer particle proposed recently by Królikowski is investigated. The radial equation derived in a previous paper is written down in the component form and reduced by eliminating auxiliary components o f the wave function. Then, the limiting behaviour at r -* 0 is checked. In the case o f the Duffin-Kemmer spin equal to 1 and the potential having the singularity r a (a > 0) it turns out that there is only one regular solution instead o f three, two o f them becoming oscillating solutions. It is shown that this phenomenon is a drastic form o f the Klein paradox. A possibility is discussed how to apply the derived radial equations to quark-diquark systems, using the regular potential emerging from the finite size of diquarks.