Eigenvalue spacing for 1D singular Schr\"odinger operators - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

Eigenvalue spacing for 1D singular Schr\"odinger operators

Luc Hillairet
Jeremy L. Marzuola
  • Fonction : Auteur

Résumé

The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schr\"odinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures related to families of Schr\"odinger operators that provides a means of establishing uniform non-concentration estimates within that class of operators. This dramatically simplifies analysis that would typically require detailed WKB expansions near the turning point, near the singular point and several gluing type results to connect various regions in the domain.

Dates et versions

hal-03604567 , version 1 (10-03-2022)

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Citer

Luc Hillairet, Jeremy L. Marzuola. Eigenvalue spacing for 1D singular Schr\"odinger operators. 2022. ⟨hal-03604567⟩
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