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.
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