2022/03/09 by Luc Hillairet, Hillairet, Luc, Jeremy L. Marzuola +1 · 1 citation
Mathematics · Physics and Astronomy · #35P20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.2203.04919
openalex publication_date 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schrödinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures related to families of Schrödinger 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.