and simplest element of the famous Mendeleev’s periodic table.

To determine the wave function of a hydrogen atom, it is useful to express the problem in the so-called variables of the *center of mass* and *relative movement*. In doing so, I will neglect for simplicity the description of the spins of the electron and proton. Without going into the details of this procedure, which can be found in any textbook of quantum mechanics, we can observe that due to this change of variables it is possible to transform the problem of two interacting bodies (electron + proton) into an effective, simpler problem, of two bodies that evolve independently of each other, and whose equations can therefore be solved separately.

The first body corresponds to the evolution of the center of mass of the system, and is equivalent to the evolution of a free entity (an entity evolving in the absence of any interaction) of total mass $M=M_e+M_p$, where $M_e$ and $M_p$ are the masses of the electron and proton, respectively. The second body corresponds instead to the evolution of a entity of (reduced) mass $\mu = M_e M_p/M$, which moves in the presence of a Coulombian central force field.

The 