On a continuum limit of discrete Schr\"odinger operators on square lattice
Mathematical Physics
2019-03-27 v1 Functional Analysis
math.MP
Spectral Theory
Abstract
The norm resolvent convergence of discrete Schr\"odinger operators to a continuum Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1903.10656,
title = {On a continuum limit of discrete Schr\"odinger operators on square lattice},
author = {Shu Nakamura and Yukihide Tadano},
journal= {arXiv preprint arXiv:1903.10656},
year = {2019}
}