### Abstract

We derive a functional equation for the Fredholm determinant of the boundary element method. By assuming that the functional equation holds for the semiclassical Fredholm determinant for strongly chaotic billiards, we obtain a real function whose zeros are the semiclassical eigenenergies. We also show by the numerical experiment of concave triangle billiards that the semiclassical eigenenergies are very close to the exact eigenenergies.

Original language | English |
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Pages (from-to) | 460-469 |

Number of pages | 10 |

Journal | Progress of Theoretical Physics Supplement |

Issue number | 139 |

DOIs | |

Publication status | Published - 2000 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

Harayama, T., Shudo, A., & Tasaki, S. (2000). A functional equation for semiclassical Fredholm determinant for strongly chaotic billiards.

*Progress of Theoretical Physics Supplement*, (139), 460-469. https://doi.org/10.1143/PTPS.139.460