The Dunkl–Duffin–Kemmer–Petiau Oscillator

In the context of the Dunkl derivative, we present the Dunkl–Duffin–Kemmer–Petiau oscillator (DDKPO) model of spin 0 and 1. For the spin 0 case , the exact solutions are determined, the wave functions are obtained using Cartesian and polar coordinates in the general form for the different eigenvalues of the reflection operators, and the corresponding spectrum energies are deduced. For the spin 1 case, the problem is complicated by the direct method, we obtain a differential equation of order four and we limit ourselves only to the study of the non-relativistic case.