PURE STATES AND P REPRESENTATION

The coherent-state P representation for the density operator of the electromagnetic field is studied for the case in which the density operator represents a pure state, ρ=|ψψ|. An exact and complete characterization is given of the states for which the P representation exists with a weight function P(α) that is a tempered distribution. These states form an exceedingly narrow class: each may be generated from a particular coherent state α by the application of a finite number of creation operators, i.e., =[c0+c1a†+»+cn(a†)n]|α where α and the cn are arbitrary complex numbers. For them the weight function P(α) is a linear combination of the two-dimensional delta function and a finite number of its derivatives. For other pure states, the function P(α) has singularities that are not compatible with the form of the P representation. © 1969 The American Physical Society.