Wigner quasi-probability distribution for the infinite square well: Energy eigenstates and time-dependent wave packets

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Abstract

We calculate and visualize the Wigner quasi-probability distribution for the position and momentum, P W (n)(x, p), for the energy eigenstates of the infinite square well. We evaluate the time-dependent Wigner distribution, P w(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.

Original languageEnglish (US)
Pages (from-to)1183-1192
Number of pages10
JournalAmerican Journal of Physics
Volume72
Issue number9
DOIs
Publication statusPublished - Sep 1 2004

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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