Bound eigenstates in two dimensions for the superposition of the Coulomb and Yukawa potentials by using the shifted 1/N method

The eigenvalue problem for an electron that is moving in a superposition of the attractive Coulomb potential - A/r and the Yukawa potential Be-λr/r is solved by using the shifted 1/N method. The calculations of the energy levels have been carried out for both cases of three and the two dimensions. The energy levels for 1s, 2p-, 3s-, 3p-, 3d- and 4f- for the two dimensions case are calculated as a function of the potential strengths A and B and the screening parameter λ. It is shown that for a given principal quantum number n, the energy eigenvalues increase (decrease) with increasing l for the 3D case and with increasing |m| for the 2D and that for 2s and 2p- levels (Lamb shift) is also discussed