Continuum limit for lattice Schrödinger operators
نویسندگان
چکیده
We study the behavior of solutions Helmholtz equation $(- \Delta_{disc,h} - E)u_h = f_h$ on a periodic lattice as mesh size $h$ tends to 0. Projecting eigenspace characteristic root $\lambda_h(\xi)$ and using gauge transformation associated with Dirac point, we show that transformed solution $u_h$ converges for $(P(D_x) E)v g$ continuous model ${\bf R}^d$, where $\lambda_h(\xi) \to P(\xi)$. For case hexagonal related lattices, {in suitable energy region}, it equation. square lattice, triangular {hexagonal (in another region)} subdivision one can add scalar potential, Schr{\"o}dinger $( +V_{disc,h} continuum + V(x) -E)u f$.
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ژورنال
عنوان ژورنال: Reviews in Mathematical Physics
سال: 2021
ISSN: ['1793-6659', '0129-055X']
DOI: https://doi.org/10.1142/s0129055x22500015