Resonances for 1D half-line periodic operators: II. Special case

2015/09/21 by Tuan Phong Trinh, Trinh, Tuan Phong
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1509.06133

27 pages, 4 figures

arxiv created 2015/09/21 · openalex publication_date 2015/09/21 · arxiv updated 2015/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper is devoted to the study of resonances for a 1D Schrödinger operator with truncated periodic potential. Precisely, we consider the half-line operator H^{\mathbb N}=-Δ+V and H^{\mathbb N}_L= -Δ+ V1_{[0, L]} acting on ℓ²(\mathbb N) with Dirichlet boundary condition at 0 with L ∈ \mathbb N. We describe the resonances of H^{\mathbb N}_L near the boundary of the essential spectrum of H^{\mathbb N} as L → +∞ under a special assumption. The present paper is in a series of our research papers on resonances

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