Gaussian wave packets in phase space: The Fermi g_F function

Abstract

Any pure quantum state can be equivalently represented by means of its wave function psi(q) or of the Fermi function g_F(q,p), with q and p coordinates and conjugate momenta of the system under investigation.We show that a Gaussian wave packet can be conveniently visualized in phase space by means of the curve g_F(q,p)=0. The evolution in time of the g_F=0 curve is then computed for a Gaussian packet evolving freely or under a constant or a harmonic force. As a result, the spreading or shrinking of the packet is easily interpreted in phase space. Finally, we 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.