Chapter 2 Density Matrix and Quantum Coherence

It is an essential postulate in quantum mechanics that the description of a system by means of wavefunction (or state vector in Hilbert space) is the most complete description possible. However, if a system under con-sideration is a part of a large closed system, we will be not able to make such a complete description because we can not write out the wavefunction for the part without complete information of the other part. In order to describe statistical concepts in quantum mechanics, von Neumann intro-duced the density matrix in 1927. The density-matrix method has been widely used in various fields of physics even till nowadays. Without the technique of density matrix, the evaluation of averages and probabilities of physical quantities for some quantum mechanical states is often a cum-bersome task. You will realize in this chapter that the density matrix is a more general representation of quantum mechanical states, which implies maximum information available for a compact mathematical formulism while avoiding the introduction of unnecessary variables. To capture the key points of the density matrix, you are suggested to start from simple systems.