論文

査読有り
2016年

Computer Assisted Verification of the Eigenvalue Problem for One-Dimensional Schrodinger Operator

MATHEMATICAL CHALLENGES IN A NEW PHASE OF MATERIALS SCIENCE
  • Ayuki Sekisaka
  • ,
  • Shunsaku Nii

166
開始ページ
145
終了ページ
157
記述言語
英語
掲載種別
研究論文(国際会議プロシーディングス)
DOI
10.1007/978-4-431-56104-0_8
出版者・発行元
SPRINGER JAPAN

We propose a rigorous computational method for verifying the isolated eigenvalues of one-dimensional Schrodinger operator containing a periodic potential and a perturbation which decays exponentially at +/-infinity. 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.


リンク情報
DOI
https://doi.org/10.1007/978-4-431-56104-0_8
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000387732800008&DestApp=WOS_CPL

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