### Abstract

We examine the long-term time dependence of Gaussian wave packets in a circular infinite well (billiard) system and find that there are approximate revivals. For the special case of purely [Formula Presented] states (central wave packets with no momentum) the revival time is [Formula Presented] where [Formula Presented] is the mass of the particle, and the revivals are almost exact. For all other wave packets, we find that [Formula Presented] and the nature of the revivals becomes increasingly approximate as the average angular momentum or number of [Formula Presented] states is increased. The dependence of the revival structure on the initial position, energy, and angular momentum of the wave packet and the connection to the energy spectrum is discussed in detail. The results are also compared to two other highly symmetrical two-dimensional infinite well geometries with exact revivals, namely, the square and equilateral triangle billiards. We also show explicitly how the classical periodicity for closed orbits in a circular billiard arises from the energy eigenvalue spectrum, using a WKB analysis.

Original language | English (US) |
---|---|

Number of pages | 1 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 65 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

### Cite this

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**Quantum wave-packet revivals in circular billiards.** / Robinett, Richard Wallace; Heppelmann, Steven.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum wave-packet revivals in circular billiards

AU - Robinett, Richard Wallace

AU - Heppelmann, Steven

PY - 2002/1/1

Y1 - 2002/1/1

N2 - We examine the long-term time dependence of Gaussian wave packets in a circular infinite well (billiard) system and find that there are approximate revivals. For the special case of purely [Formula Presented] states (central wave packets with no momentum) the revival time is [Formula Presented] where [Formula Presented] is the mass of the particle, and the revivals are almost exact. For all other wave packets, we find that [Formula Presented] and the nature of the revivals becomes increasingly approximate as the average angular momentum or number of [Formula Presented] states is increased. The dependence of the revival structure on the initial position, energy, and angular momentum of the wave packet and the connection to the energy spectrum is discussed in detail. The results are also compared to two other highly symmetrical two-dimensional infinite well geometries with exact revivals, namely, the square and equilateral triangle billiards. We also show explicitly how the classical periodicity for closed orbits in a circular billiard arises from the energy eigenvalue spectrum, using a WKB analysis.

AB - We examine the long-term time dependence of Gaussian wave packets in a circular infinite well (billiard) system and find that there are approximate revivals. For the special case of purely [Formula Presented] states (central wave packets with no momentum) the revival time is [Formula Presented] where [Formula Presented] is the mass of the particle, and the revivals are almost exact. For all other wave packets, we find that [Formula Presented] and the nature of the revivals becomes increasingly approximate as the average angular momentum or number of [Formula Presented] states is increased. The dependence of the revival structure on the initial position, energy, and angular momentum of the wave packet and the connection to the energy spectrum is discussed in detail. The results are also compared to two other highly symmetrical two-dimensional infinite well geometries with exact revivals, namely, the square and equilateral triangle billiards. We also show explicitly how the classical periodicity for closed orbits in a circular billiard arises from the energy eigenvalue spectrum, using a WKB analysis.

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U2 - 10.1103/PhysRevA.65.062103

DO - 10.1103/PhysRevA.65.062103

M3 - Article

VL - 65

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

ER -