arXiv:2006.15593v1 [quant-ph] 28 Jun 2020 Scalar and Vector Bosonic oscillator in 3D Spaces with Extended Uncertainty Principle Mokhtar FALEK 1 Mustafa MOUMNI 1,2 Mahmoud MERAD 3 m.moumni@univ-biskra.dz 1 Laboratory of Photonic Physics and Nano-Materials (LPPNNM) Department of Matter Sciences, University of Biskra, ALGERIA 2 Laboratory of Radiations and Matter (PRIMALAB) Department of Physics, University of Batna, ALGERIA Faculty of Exact Sciences, University of Oum-el-Bouaghi, ALGERIA June 30, 2020 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. Keywords: DKP oscillator; Anti–de Sitter space; Three dimensions P. A. C. S. 03.65.Ge, 03.65.Pm. Contents 1 Introduction 2 2 Review of the deformed quantum mechanics relation 3 3 Nikiforov–Uvarov method 4 4 Spin 0 DKP Oscillator 5 5 Spin 1 DKP Oscillator 10 5.1 Natural Parity States .................................... 12 5.2 Unnatural Parity States .................................. 13 6 Conclusion 18 1