The hydrogen atom
The hydrogen atom is a very important problem in quantum mechanics. It is also a problem described by Schrödinger’s equation that is mathematically exactly solvable (if we neglect a few small corrections that lie beyond the simple Schrödinger equation description).1 These solutions give the basis for our conceptual understanding of atoms and molecules, as well as much of the notation. In engineering, the hydrogen atom solutions also can be used as a model to explain a phenomenon (i.e., Wannier excitonic effects) that is very important in the optical absorption in most semiconductor optoelectronic devices.
The hydrogen atom problem is additionally an excellent tutorial one ...