On a continuum limit of discrete Schrödinger operators on square lattice

2019/03/26 by Shu Nakamura, Nakamura, Shu, Yukihide Tadano +1 · 1 citation
Mathematics · #47A10 #47A58 #81Q35 #Advanced Mathematical Physics Problems #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1903.10656

openalex publication_date 2019/03/26 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28

Abstract

The norm resolvent convergence of discrete Schrödinger operators to a continuum Schrödinger operator in the continuum limit is proved under relatively weak assumptions. This result implies, in particular, the convergence of the spectrum with respect to the Hausdorff distance.

Citations

• Strong Convergence for Discrete Nonlinear Schrödinger equations in the Continuum Limit

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