Overview
The hydrogen atom consists of a single positively charged heavy particle, the proton in the nucleas of the atom, and a lighter particle, an electron, that is negatively charged and moves in an orbit around the nuclues.
Because the proton is much heavier than the electron, it can assumed to be fixed at the origin of a coordinate system. The model then becomes a model of the electron in the presence of the proton.
The primary interaction between the two will be electro-magnetic in nature. In particular, the electron is subject to a potential of the form
{% V(r) = - \frac{e^2}{4 \pi \epsilon_0} \frac{1}{r} %}