Relativistic Energy Analysis Of Five Dimensional q-Deformed Radial Rosen-Morse Potential Combined With q-Deformed Trigonometric Scarf Non-Central Potential Using Asymptotic Iteration Method (AIM)

TL;DR

This paper derives exact solutions for the Dirac equation with q-deformed potentials in five dimensions using AIM, revealing how energy levels depend on quantum numbers and deformation parameters.

Contribution

It introduces a novel application of AIM to solve the Dirac equation with combined q-deformed potentials in five dimensions, providing explicit energy and wave function solutions.

Findings

Relativistic energy levels increase with radial quantum number n.

Energy levels decrease as deformation parameter q increases.

Bound states are affected by both quantum numbers and deformation parameters.

Abstract

In this work, we study the exact solution of Dirac equation in the hyper-spherical coordinate under influence of separable q-Deformed quantum potentials. The q-deformed hyperbolic Rosen-Morse potential is perturbed by q-deformed non-central trigonometric Scarf potentials, where whole 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 lD-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 Mat Lab, the increase of radial quantum number n causes the increase of bound state relativistic energy level both in dimension D = 5 and D = 3. The bound state relativistic energy level decreases with increasing of both deformation parameter q and orbital quantum number nl.