Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators

Kaori Nagatou, Michael Plum*, Mitsuhiro T. Nakao

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

Subject of investigation in this paper is a one-dimensional Schrödinger equation, where the potential is a sum of a periodic function and a perturbation decaying at ±∞. It is well known that the essential spectrum consists of spectral bands, and that there may or may not be additional eigenvalues below the lowest band or in the gaps between the bands. While enclosures for gap eigenvalues can comparatively easily be obtained from numerical approximations, e.g. by D. Weinstein's bounds, there seems to be no method available so far which is able to exclude eigenvalues in spectral gaps, i.e. which identifies subregions (of a gap) which contain no eigenvalues. Here, we propose such a method. It makes heavy use of computer assistance; nevertheless, the results are completely rigorous in the strict mathematical sense, because all computational errors are taken into account.

本文言語English
ページ(範囲)545-562
ページ数18
ジャーナルProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
468
2138
DOI
出版ステータスPublished - 2012 2 8
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)
  • 工学(全般)
  • 物理学および天文学(全般)

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