Abstract
We successfully obtained the complete exact solution of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-1 bosons in (1+2)-dimensional space time using a 10×10 representation of the beta-matrices. We show that the problem can be decoupled into three independent subproblems, each of which is assigned with one of the spin-projection numbers ms=0 and ms=±1. Moreover, the solutions such that ms=0 and those for which ms=±1 are found to be respectively associated with (−1)J and (−1)J+1 parities. In addition, we investigate the effect of the presence of an external transverse homogeneous magnetic field on the dynamics of the oscillator: different settings, as well as interesting particular cases, are considered and the non-relativistic limit of the model is also discussed.
•The complete solution of the vector DKP oscillator in 2D are obtained.•The problem is shown to decouple into three independent subproblems.•Effects of applying an external homogeneous magnetic field are investigated.