Non-relativistic and relativistic equations for the Kratzer potential plus a dipole in 2D systems

In this work, we study the wave equations in 2D Euclidian space for a new non-central potential consisting of a Kratzer term and a dipole term V (r, theta) = Qr(-1) + D-r r(-2) + D-theta cos(theta)r(-2). For Schrodinger equation, we obtain the analytical expressions of the energies and the wave functions of the system. For Klein-Gordon and Dirac equations, we do the study in both spin and pseudo-spin symmetries to get the eigenfunctions and the eigenvalues. We also study the dependence of energies on the parameters D-r and D-theta. We find that the D-theta term tends to dissociate the system, and thus counteracts the Coulomb binding effect, and that the D-r term can either amplify or decrease this effect according to its sign.