In this work, an analytical approximate solution of the Pauli equation with a Deng-Fan potential under the influence of the Aharonov-Bohm effect has been studied using the generalized Nikiforov-Uvarov (NU) parametric method. In this research, mathematical and physical methods are employed to calculate the wave function for different states of the system. After obtaining the wave functions, special energy values can be computed for regions where r>R and r<R by considering boundary conditions and continuity in the region r=R. This research employs the NU method, a versatile tool for solving second-order differential equations. The Pauli equation, crucial in describing fermions with spin ½, is explored within the context of the Deng-Fan potential and the Aharonov-Bohm effect. Originating from the non-relativistic limit of the Dirac equation, the Pauli equation has historical significance in quantum theory's development. This study addresses its application in two dimensions with the Deng-Fan potential and the Aharonov-Bohm effect, considering a constrained and non-zero magnetic field. Eigenenergy values and eigenfunctions are obtained using the NU method, revealing wave functions for different regions. Results illustrate the wave function's behavior, showcasing its decrease with increasing radial distance and increase with angular momentum. The Deng-Fan potential emerges as an intriguing option for theoretical physicists studying molecular systems. Qualitatively resembling the Morse potential, it proves compatible with quantum requirements and is suitable for investigating physical systems alongside Coulomb or linear potentials. The study contributes an approximate analytical solution for the Pauli equation's eigenwave functions, enhancing understanding of quantum systems under molecular potentials and advancing quantum physics knowledge.
