  By using a Coulomb potential modified by the interaction between the magnetic
moments of the electron and proton, we have calculated the energy levels of a
hydrogen atom. We have obtained fine structure, hyperfine structure and the
Lamb shift. All these are obtained from a simple formula which is a direct
solution of the Schroedinger equation. The obtained results are in a good
agreement with experimental data. For example, the hyperfine splitting between
the energy levels of the states 1S1/2,1 and 1S1/2,0 is of the order of
5.6x10^(-6) eV, which is the source of the famous "21 cm line" which is
strongly useful to radio astronomers for tracking hydrogen in the interstellar
medium of galaxies. The energy of the states nP1/2 is lower than those of the
states nS1/2 (Lamb shift), because in the first case the interaction between
the magnetic moments of the proton and electron spins is diminished by the
spin-orbit coupling.
