The density matrix
The density operator or, as it is more commonly called, the density matrix, is a key tool in quantum mechanics that allows us to connect the world of quantum mechanics with the world of statistical mechanics and we introduce it briefly here. This is an important connection. Just as we needed statistical ideas in complicated classical systems (e.g., large collections of atoms or molecules), we need the same ideas in complicated quantum mechanical systems.
We also examine one elementary but important application in optics: we use the density matrix to turn the extreme and unrealistic idea of infinitely sharp “δ-function” optical transitions that emerged ...