An effective singular oscillator for Duffin-Kemmer-Petiau particles with   a nonminimal vector coupling: a two-fold degeneracy
  Scalar and vector bosons in the background of one-dimensional nonminimal vector linear plus inversely linear potentials are explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. The problem is mapped into a Sturm-Liouville problem with an effective singular oscillator. With boundary conditions emerging from the problem, exact bound-state solutions in the spin-0 sector are found in closed form and it is shown that the spectrum exhibits degeneracy. It is shown that, depending on the potential parameters, there may or may not exist bound-state solutions in the spin-1 sector. 
T.R. Cardoso, L.B. Castro, A.S. de Castro
hep-th quant-ph