By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary m-state in two-dimensional Schrödinger wave equation with various power interaction potentials in constant magnetic and Aharonov-Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We calculate the energy levels of some diatomic molecules in the presence and absence of external magnetic and AB flux fields using different potential models. We found that the effect of the Aharonov-Bohm field is much as it creates a wider shift for m = 0 and its influence on m = 0 states is found to be greater than that of the magnetic field. To show the accuracy of the present model, a comparison is made with those ones obtained in the absence of external fields. An extension to 3-dimensional quantum system have also been presented.1 describing the molecular vibrations is important in studying the dynamical variables of diatomic molecules [3]. This potential have a wide applications in various fields of physics and chemistry such as molecular physics, solid-state physics, chemical physics, quantum chemistry, the molecular dynamics study of linear diatomic molecules and the theoretical works on the spectral properties of a diatomic molecule system [4]. Therefore, we found that it is necessary to study the exact bound state solutions of the two-dimensional (2D) solution of the Schrödinger equation for these potentials under the influence of external magnetic and Aharonov-Bohm fields. The 2D hydrogen model was treated as an atomic spectroscopy and used as a simplified model of the ionization process of the highly excited 3D hydrogen atom by circular-polarized microwaves [5]. The field-free relativistic Coulomb interaction has been studied by many authors by using various techniques [6, 7, 8]. The nonrelativistic H-like atom under the influence of magnetic field has been the subject of study over the past years [9, 10, 11]. In the presence of a low magnetic field, the quasi-classical solution of the Dirac equation has been obtained by factorization method [12]. In the framework of the variational method, the ground-state Dirac energies and relativistic spinless lowest few states have been calculated for arbitrary strength values of magnetic field [13, 14, 15]. The Klein-Gordon wave equation was solved exactly for particular values of magnetic field in which the wave function can be expressed in closed analytical form [16]. The polynomial solutions of the Schrödinger equation was obtained for the ground-state and a few first excited states of 2D hydrogenic atoms for particular values of the magnetic field strength perpendicular to the plane of transversal motion of the electron using a relativistic wave function [17]. Recently, within the framework of power-series solutions, the Klein-Gordon and Dirac equations have beensolved for the 2D hydrogen-like systems when an arbitrary external magnetic field is applied [18]. For particular values of magnetic field B, it is found that the exact ...
