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By using a Coulomb potential modified by the interaction between the magneticmoments of the electron and proton, we have calculated the energy levels of ahydrogen atom. We have obtained fine structure, hyperfine structure and theLamb shift. All these are obtained from a simple formula which is a directsolution of the Schroedinger equation. The obtained results are in a goodagreement with experimental data. For example, the hyperfine splitting betweenthe energy levels of the states 1S1/2,1 and 1S1/2,0 is of the order of5.6x10^(-6) eV, which is the source of the famous "21 cm line" which isstrongly useful to radio astronomers for tracking hydrogen in the interstellarmedium of galaxies. The energy of the states nP1/2 is lower than those of thestates nS1/2 (Lamb shift), because in the first case the interaction betweenthe magnetic moments of the proton and electron spins is diminished by thespin-orbit coupling.

Evaluation of the energy states of hydrogen atom using Schroedinger  equation with a Coulomb potential modified by the interaction between the  magnetic moments of the proton and electron