The Kemmer Oscillator with Minimal Length and Noncommutative Phase Space in two dimensions

We investigate the twodimensional DuffinKemmerPetiau (DKP) oscillator in a deformed phase space that incorporates both noncommutative spatial coordinates and momenta, together with a minimal length induced by the generalized uncertainty principle (GUP).Working in momentum space, the DKP system is decoupled and the resulting radial equation is reduced to a Gauss hypergeometric differential equation. This procedure yields closed-form wave functions together with an exact algebraic quantization condition for the energy spectrum. Because the noncommutative contributions introduce explicit energy dependence, the spectral equation is implicit in the energy and must be solved numerically for fixed parameter values. The dependence of the spectrum on the minimal-length parameter [Formula: see text] and the noncommutative parameters [Formula: see text] is analyzed in detail. The results show that [Formula: see text] primarily governs the overall curvature of the spectrum as a function of the radial quantum number, whereas [Formula: see text] mmodify the effective oscillator scale and alter the spacing between neighboring levels. Relevant limiting cases are discussed, and the role of the reducible [Formula: see text] DKP representation employed in the calculation is clarified.