2021/12/07 by А. А. Шкаликов, A. A. Shkalikov, Shkalikov, A. A. +2
Mathematics · Physics and Astronomy · #34Mxx #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #math-ph #math.CA #math.MP #math.SP #msc:34Mxx
paper · pdf · doi:10.48550/arxiv.2112.03743
arxiv created 2021/12/07 · openalex publication_date 2021/12/07 · arxiv updated 2021/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Sturm--Liouville operator T(ε)y=-(1)/(ε)y''+ p(x)y, with concrete PT-- symmetric potential p(x) = ix and Dirichlet boundary conditions on the segment [-1,1]. Here ε ∈ (0, ∞) is a physical parameter. We explicitly describe a beautiful phenomenon of the eigenvalue behavior when ε changes from 0 to ∞. All the critical values of ε which determine the eigenvalue dynamics, are found in terms of the special Airy functions.