### 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) |
---|---|

Pages (from-to) | 1183-1192 |

Number of pages | 10 |

Journal | American Journal of Physics |

Volume | 72 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

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*American Journal of Physics*, vol. 72, no. 9, pp. 1183-1192. https://doi.org/10.1119/1.1767100

**Wigner quasi-probability distribution for the infinite square well : Energy eigenstates and time-dependent wave packets.** / Belloni, M.; Doncheski, M. A.; Robinett, R. W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Wigner quasi-probability distribution for the infinite square well

T2 - Energy eigenstates and time-dependent wave packets

AU - Belloni, M.

AU - Doncheski, M. A.

AU - Robinett, R. W.

PY - 2004/9/1

Y1 - 2004/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=4544273266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544273266&partnerID=8YFLogxK

U2 - 10.1119/1.1767100

DO - 10.1119/1.1767100

M3 - Article

AN - SCOPUS:4544273266

VL - 72

SP - 1183

EP - 1192

JO - American Journal of Physics

JF - American Journal of Physics

SN - 0002-9505

IS - 9

ER -