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We study the exact solution of Dirac equation in the hyperspherical coordinate under influence of separable q -deformed quantum potentials. The q -deformed hyperbolic Rosen-Morse potential is perturbed by q -deformed noncentral trigonometric Scarf potentials, where all of them can be solved by using Asymptotic Iteration Method (AIM). This work is limited to spin symmetry case. The relativistic energy equation and orbital quantum number equation l D - 1 have been obtained using Asymptotic Iteration Method. The upper radial wave function equations and angular wave function equations are also obtained by using this method. The relativistic energy levels are numerically calculated using Matlab, and the increase of radial quantum number n causes the increase of bound state relativistic energy level in both dimensions D = 5 and D = 3 . The bound state relativistic energy level decreases with increasing of both deformation parameter q and orbital quantum number n l .

advances in high energy physics

Relativistic Energy Analysis of Five-Dimensional q-Deformed Radial Rosen-Morse Potential Combined with q-Deformed Trigonometric Scarf Noncentral Potential Using Asymptotic Iteration Method