Square wells, quantum wells and ultra-thin metallic films

The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these results in the physics of quantum wells are discussed, especially for ultra-thin metallic films, but also in the case of resonant cavities, heterojunction lasers, revivals and super-revivals.