Accurate iterative solution of the energy eigenvalues of a two-dimensional hydrogenic donor in a magnetic field of arbitrary strength

In this paper, we present the energy eigenvalues of a two-dimensional hydrogenic donor in a magnetic field by using the asymptotic iteration method. The binding energy eigenvalues in the presence of weak and strong magnetic fields (γ≠0) are obtained within the framework of this iterative approach for 1S, 2P- and 3D- levels. The energy eigenvalues for the non-magnetic field case (γ=0) are also determined and the results are compared with the values in weak and strong magnetic fields. The effect of the magnetic field strength on the energy eigenvalues are determined explicitly and excellent agreement with the findings of other methods is obtained.