2003/12/09 by M. Belloni, M. A. Doncheski, R. W. Robinett · 1 citation
Physics and Astronomy · #Distribution (mathematics) #Eigenvalues and eigenvectors #Energy (signal processing) #Gaussian #Position (finance) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum many-body systems #Square (algebra) #Wave packet #Wigner distribution function #quant-ph
paper · pdf · doi:10.1119/1.1767100
45 pages, 16 embedded, low-resolution .eps figures (higher resolution, publication quality figures are available from the authors); submitted to American Journal of Physics
arxiv created 2003/12/09 · openalex publication_date 2004/08/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We calculate and visualize the Wigner quasi-probability distribution for the position and momentum, PW(n)(x,p), for the energy eigenstates of the infinite square well. We evaluate the time-dependent Wigner distribution, PW(x,p;t), for Gaussian wave packet solutions of this system, and illustrate the short-term semi-classical time dependence and the longer-term revival and fractional revival behavior. Our results indicate how the Wigner distribution can be used to examine the highly correlated dynamical position-momentum structure of quantum states. In particular, this tool provides an excellent way of demonstrating the patterns of highly correlated Schrödinger-cat-like “mini-packets” which appear at fractional multiples of the exact revival time.