An Agmon estimate for Schrödinger operators on graphs
نویسندگان
چکیده
The Agmon estimate shows that eigenfunctions of Schrödinger operators, $$ -\Delta \phi + V = E , decay exponentially in the ‘classically forbidden’ region where potential exceeds energy level $$\left\{ x: V(x) > \right\} . Moreover, size $$|\phi (x)|$$ is bounded terms a weighted (Agmon) distance between x and allowed region. We derive such statement on graphs when $$-\Delta replaced by graph Laplacian $$L D-A$$ : we identify an explicit metric prove pointwise distance.
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2023
ISSN: ['0377-9017', '1573-0530']
DOI: https://doi.org/10.1007/s11005-023-01635-5