Gaussian wave packets in phase space : the Fermi g(F) function

A pure quantum state can be equivalently represented by means of its wave function psi(q) or by the Fermi function g(F)(q,p), with q and p coordinates and conjugate momenta of the system of interest. We show that a Gaussian wave packet can be conveniently visualized in phase space by the curve g(F)(q,p)=0. The change in time of the g(F)=0 curve is calculated for a Gaussian packet evolving freely or under a constant or a harmonic force, and the spreading or shrinking of the packet is easily interpreted in phase space. We also discuss a gedanken prism microscope experiment for measuring the position-momentum correlation. This gedanken experiment, together with the well-known Heisenberg microscope and von Neumann velocimeter, is sufficient to fully determine the state of a Gaussian packet.