2008/10/31 by Giuliano Benenti, Giuliano Strini
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1119/1.3083268
published as Am. J. Phys. 77, 546 (2009) · 7 pages, 4 figures, remarks added
arxiv created 2008/12/08 · openalex publication_date 2009/05/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A pure quantum state can be equivalently represented by means of its wave function ψ(q) or by the Fermi function gF(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 gF(q,p)=0. The change in time of the gF=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.