Spin-1/2 Pauli equation with Woods–Saxon potential in the presence of Aharonov–Bohm Coulomb problem in non-commutative space

In this paper, we consider the spin-1/2 Pauli equation under the influence of an Aharonov–Bohm (AB) Coulomb problem with the Woods–Saxon potential in the relativistic quantum mechanics framework. We obtained the eigenfunctions and the corresponding numerical bound state energies. We see that the AB effect lifts the degeneracy of energy levels. Therefore, we found the Pauli equation for a spin-1/2 particle in the background of an electromagnetic field in noncommutative space. The effect of space noncommutativity on the Pauli equation has been successfully observed.