Computer assisted verification of the eigenvalue problem for one-dimensional Schrödinger operator

Ayuki Sekisaka, Shunsaku Nii

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

We propose a rigorous computational method for verifying the isolated eigenvalues of one-dimensional Schrödinger operator containing a periodic potential and a perturbation which decays exponentially at ±∞. We show how the original eigenvalue problem can be reformulated as the problem of finding a connecting orbit in a Lagrangian-Grassmanian. Based on the idea of the Maslov theory for Hamiltonian systems, we set up an integer-valued topological measurement, the rotation number of the orbit in the resulting one-dimensional projective space. Combining the interval arithmetic method for dynamical systems, we demonstrate a computer-assisted proof for the existence of isolated eigenvalues within the first spectral gap.

本文言語英語
ホスト出版物のタイトルMathematical Challenges in a New Phase of Materials Science
編集者Yasumasa Nishiura, Motoko Kotani
出版社Springer New York LLC
ページ145-157
ページ数13
ISBN(印刷版)9784431561026
DOI
出版ステータス出版済み - 2016
イベントInternational Conference on Mathematical Challenges in a New Phase of Materials Science, 2014 - Kyoto, 日本
継続期間: 8 4 20148 8 2014

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
166
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

その他

その他International Conference on Mathematical Challenges in a New Phase of Materials Science, 2014
国/地域日本
CityKyoto
Period8/4/148/8/14

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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