The Duffin-Kemmer-Petiau oscillator

In view of the current interest in relativistic spin-1 systems and the recent work on the Dirac oscillator, we introduce the Duffin-Kemmer-Petiau (DKP) equation obtained by using an external potential linear in r. Since the spin-0 representation leads to a harmonic oscillator in the non-relativistic limit and becomes an harmonic oscillator with a spin-orbit coupling of the Thomas form for vector bosons, we call the equation the DKP oscillator. This oscillator is a relativistic generalization of the quantum harmonic oscillator for scalar and vector bosons. We show that it conserves total angular momentum and that it is exactly solvable for both scalar and vector DKP bosons. We calculate and discuss the eigenvalues and eigenstates of the DKP oscillator in the spin-0 and spin-1 representations.