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.

中文翻译：

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关于方格上离散Schrödinger算子的连续极限

在相对弱的假设下，证明了离散薛定ding算子到连续薛定ding算子在连续极限中的范数可分解收敛。该结果尤其意味着频谱相对于Hausdorff距离的收敛。