Relativistic two-body equation for one Dirac and one Klein-Gordon particle

A new relativistic two-body wave equation is conjectured for a system of one Dirac and one Klein-Gordon particle. The equation is solved exactly for Coulombic bound states in the case of equal, non-zero masses. In particular, a massless stable Coulombic bound state with j=1/2 is shown to exist, provided the coupling constant α assumes its critical value 2. Such a situation would appear for every unbroken supersymmetric massive pair of one Dirac and one Klein-Gordon particle if only they interacted mutually through a critical Coulombic field. (author)