The Vector Planar DKP Oscillator Within a Minimal Length Uncertainty Relation

In this work, we investigate the solutions of the two-dimensional Duffin–Kemmer–Petiau oscillator for spin-one particles under a minimal length assumption. To incorporate the minimal length, we assume a generalized uncertainty principle with two deformation parameters implying a noncommutative phase space. By employing the momentum representation, we were able to solve the problem exactly for all spin projection numbers and obtain the minimal length corrections brought to the energy eigenvalues and the associated eigenstates of the oscillator. The solutions are systematically classified into natural and unnatural parity states contingent upon the spin-projection numbers. Additionally, we studied the effect of applying an external transverse homogeneous magnetic field (HMF) on the dynamics of the system. In particular, the motion of a spin-one boson moving in the plane under a HMF is considered as a special case. We also discuss the nonrelativistic limit of the energy eigenvalues in each one of the considered instances.