### 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 language | English (US) |
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Pages (from-to) | 1183-1192 |

Number of pages | 10 |

Journal | American Journal of Physics |

Volume | 72 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)