The preceding chapters provide a detailed mathematical description of the properties of a single particle constrained in space by potentials of various geometries. There are clear trends that emerge which allow us to think about the effect of quantum confinement. However, applications to more realistic systems require that we think further about systems with multiple electrons. Unfortunately, accurate descriptions of multi-electron systems are very complex because the electrons interact with each other. It is beyond the purpose of this text to deal properly with electron interactions, but we will consider some idealized systems that provide reasonable first approximations and illustrate the principles that we need to understand.