Continuum limit for lattice Schrödinger operators

@article{Isozaki2021ContinuumLF,
  title={Continuum limit for lattice Schr{\"o}dinger operators},
  author={Hiroshi Isozaki and Arne Jensen},
  journal={Reviews in Mathematical Physics},
  year={2021}
}
We study the behavior of solutions of the Helmholtz equation [Formula: see text] on a periodic lattice as the mesh size [Formula: see text] tends to 0. Projecting to the eigenspace of a characteristic root [Formula: see text] and using a gauge transformation associated with the Dirac point, we show that the gauge transformed solution [Formula: see text] converges to that for the equation [Formula: see text] for a continuous model on [Formula: see text], where [Formula: see text]. For the case… 

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