Schroedinger wave operators on the discrete half-line

2019/07/07 by Hideki Inoue, Inoue, Hideki, Naohiro Tsuzu +1 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1907.03243

openalex publication_date 2019/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An explicit formula for the wave operators associated with Schroedinger operators on the discrete half-line is deduced from their stationary expressions. The formula enables us to understand the wave operators as one dimensional pseudo-differential operators of order zero. As an application, we give a topological interpretation for Levinson's theorem, which relates the scattering phase shift and the number of bound states of the system.

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• Topological Levinson's theorem and corrections at thresholds: the full picture in a quasi-1D example

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