论文标题
Agmon估算了Schrödinger操作员的图表
An Agmon estimate for Schrödinger operators on Graphs
论文作者
论文摘要
Agmon估计表明，schrödinger操作员的特征函数，$ -Δϕ+ v ϕ = e ϕ $，在“经典禁止”区域中呈指数衰减，其中电势超过能量水平$ \ left $ \ left \ eft \ {x：v（x）：v（x）> e \ right \ right \} $。此外，$ | ϕ（x）| $的大小是根据$ x $和允许区域之间的加权（agmon）距离界定的。当$-δ$被图形laplacian $ l = d-a $取代时，我们会在图形上得出这样的陈述：我们确定了一个明确的agmon公制，并证明了在agmon距离方面的刻度衰减估计值。
The Agmon estimate shows that eigenfunctions of Schrödinger operators, $ -Δϕ+ V ϕ= E ϕ$, decay exponentially in the `classically forbidden' region where the potential exceeds the energy level $\left\{x: V(x) > E \right\}$. Moreover, the size of $|ϕ(x)|$ is bounded in terms of a weighted (Agmon) distance between $x$ and the allowed region. We derive such a statement on graphs when $-Δ$ is replaced by the Graph Laplacian $L = D-A$: we identify an explicit Agmon metric and prove a pointwise decay estimate in terms of the Agmon distance.
