DKP spin-one particles confined in a two-dimensional ring

Abstract

We study the confinement of relativistic spin-one particles in two spatial dimensions by a quantum ring for systems described by the Duffin–Kemmer–Petiau (DKP) equation. The ring-like geometry is realized by introducing a pseudo-scalar funnel-shape potential into the DKP equation, leading to a generalization of the planar DKP oscillator. Having used a ten-dimensional representation of the DKP matrices, the DKP equation is then mapped into two uncoupled subproblems, the first is associated with states of zero spin-projection (natural parity states) and the second is associated with states having a spin-projection number equal to ±1 (unnatural parity states). For both subproblems the exact wave functions of the system are analytically derived and expressed through the generalized Laguerre polynomials. The corresponding energy eigenvalues are explicitly obtained for natural parity states, while in the unnatural parity case an exact energy equation from which they can be determined is derived.