where we set ∂j = ∂/∂xj and xj = x+, xz, x. For example, we obtain after some calculation



for the Perelomov coherent state and



for the Barut–Girardello coherent state



for the atomic coherent state.

Next, we consider average values in a quantum state described by the density operator ρ



where Z = Tr exp(a+K+ + azKz + aK) with Tr being the trace operation. The parameters a± and az are required such that the density operator ρ

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