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

Abstract

The eigenvalue problem for an electron that is moving in a superposition of the attractive Coulomb potential and the Yukawa potential 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.