Exact Solutions of the DKP Oscillator in 3D Spaces with Extended Uncertainty Principle

TL;DR

This paper provides exact solutions for the 3D DKP oscillator incorporating minimal momentum uncertainty in an anti-de Sitter space, revealing new insights into parity states and spin-orbit effects.

Contribution

It offers the first exact solutions for the 3D DKP oscillator with extended uncertainty principle, analyzing energy spectra and parity distinctions.

Findings

Exact energy eigenvalues and eigenfunctions derived

New interpretation of parity states based on spin-orbit coupling

Role of minimal momentum uncertainty in the spectrum

Abstract

We present the exact solution of the three-dimensional Duffin--Kemmer--Petiau oscillator for both spin 0 and spin 1 cases, with the presence of minimal uncertainty in momentum in anti--de Sitter model. We use the representation of vector spherical harmonics and the Nikiforov--Uvarov method to determine exactly the energy eigenvalues and the eigenfunctions in all cases. Our study of the energy spectrum allows us to define a new interpretation of natural and unnatural parity states of the vector particle and we show the crucial role played by the spin--orbit coupling in this differentiation between the parities.