The spin-one DKP oscillator with an extra spin–orbit coupling

Abstract

We consider a generalization of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-1 bosons, built by implementing an extra spin–orbit coupling (SOC) into the standard DKPO equation. This model meets the requirements of Lorentz covariance as well as the existence of a conserved four-current, and is found to be exactly solvable for both natural and unnatural parity states and for an arbitrary total angular momentum number. The obtained energy eigenvalues show that the additional SOC brings about radical modifications in the spectroscopy of the DKPO. Notably, the spin–orbit splitting of the energy levels becomes controllably independent from oscillator shells. Moreover, interesting particular cases of the model as well as its non-relativistic limit are discussed.