Scattering and bound states of spin-0 particles in a nonminimal vector double-step potential

The problem of spin-0 particles subject to a nonminimal vector double-step potential is explored in the context of the Duffin-Kemmer-Petiau theory. Surprisingly, one can never have an incident wave totally reflected and the transmission amplitude has complex poles corresponding to bound states. The interesting special case of bosons embedded in a sign potential with its unique bound-state solution is analyzed as a limiting case.