Can One Determine the Shape of a Quantum Billiard Table through the Eigenenergies and Resonances?

Yuichiro Okada*, Akira Shudo, Takahisa Harayama, Shuichi Tasaki

*この研究の対応する著者

研究成果: Article査読

抄録

The quantum billiard problem, that is the Dirichlet problem for the Helmholtz equation, can be rewritten as a Fredholm integral equation of the second kind and the eigenenergies can be characterized as the zeros of the Fredholm determinant on the positive real axis. However the Fredholm determinant also has complex zeros corresponding to the resonances when the billiard table is regarded as a scatterer against the exterior wave function. That naturally leads us to a new question "Can one determine the shape of billiard table through the interior eigenenergies and exterior resonances, i.e., all zeros of the Fredholm determinant?" instead of the famous Kac's question "Can one hear the shape of a drum?", which was solved negatively.

本文言語English
ページ(範囲)397-400
ページ数4
ジャーナルProgress of Theoretical Physics Supplement
150
DOI
出版ステータスPublished - 2003
外部発表はい

ASJC Scopus subject areas

  • 物理学および天文学(その他)

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