  We make a comparison between the energy levels of the hydrogen atom,
calculated by using standard methods, and that by using a modified Coulomb
potential due to the interaction between the magnetic moments of the proton and
electron. In this later method we use to ways. One is that in which we solve
the Schroedinger equation with the modified Coulomb potential and some
constraint conditions. The other is that in which we expand the modified
Coulomb potential in Taylor series. The obtained results show that the first
way gives a better agreement with experimental data.
