Abstract
We study a covariant extension of the spin-one DuffinKemmerPetiau (DKP) oscillator constructed by combining a Lorentz tensor spin–orbit coupling with the basic DKP oscillator one. We show that this model has a spin-orbit splitting controllably independent from oscillator shells and admits exact analytical solutions for both natural and unnatural parity states. The corresponding energy spectrum is then obtained for any value of the total angular momentum number and a drastic change in its structure is observed due to the additional spin–orbit coupling. In particular energy bounds and, in some cases, forbidden energy ranges are noted.
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