### Abstract

Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by T_{rev}=9μa^{2}/4ℏπ where a and μ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60°-60°-60°) triangle, such as the half equilateral (30°-60°-90°) triangle and other "foldings," which have related energy spectra and revival structures.

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

Pages (from-to) | 208-227 |

Number of pages | 20 |

Journal | Annals of Physics |

Volume | 299 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

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**Quantum mechanical analysis of the equilateral triangle billiard : Periodic orbit theory and wave packet revivals.** / Doncheski, Michael; Robinett, Richard Wallace.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum mechanical analysis of the equilateral triangle billiard

T2 - Periodic orbit theory and wave packet revivals

AU - Doncheski, Michael

AU - Robinett, Richard Wallace

PY - 2002/8/1

Y1 - 2002/8/1

N2 - Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by Trev=9μa2/4ℏπ where a and μ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60°-60°-60°) triangle, such as the half equilateral (30°-60°-90°) triangle and other "foldings," which have related energy spectra and revival structures.

AB - Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by Trev=9μa2/4ℏπ where a and μ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60°-60°-60°) triangle, such as the half equilateral (30°-60°-90°) triangle and other "foldings," which have related energy spectra and revival structures.

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U2 - 10.1006/aphy.2002.6276

DO - 10.1006/aphy.2002.6276

M3 - Article

VL - 299

SP - 208

EP - 227

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -