Partial differential equation hydrogen atom

The equation that, in principle, describes the behavior of electrons in atoms and molecules is the Schrodinger equation (SE). This equation can only be solved exactly for the simplest atom, namely, hydrogen. This circumstance has led to major intellectual efforts to obtain increasingly more accurate solutions to this equation for systems of a wide variety of interest. The SE is a partial differential equation in 3n+3N variables. Here n refers to the number of electrons, and N gives the number of nuclei of the system. For atoms, the number of nuclei is trivial, but... 

The Schrodinger equation for the hydrogen atom is a second-order partial differential equation in three variables. A customary technique for solving this type of differential equation is by a procedure known as the separation of variables. In that way, a complicated... 

---