WKB Asymptotic Behavior of Almost All Generalized Eigenfunctions for One-Dimensional Schrödinger Operators with Slowly Decaying Potentials
WKB Asymptotic Behavior of Almost All Generalized Eigenfunctions for One-Dimensional Schrödinger Operators with Slowly Decaying Potentials
复制标题
具有缓慢衰减势的一维薛定谔算子的几乎所有广义本征函数的 WKB 渐近行为
DOI：
10.1006/jfan.2000.3688
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发表时间：
2001
影响因子：
1.7
通讯作者：
A. Kiselev
中科院分区：
文献类型：
--
作者：
Michael Christ;A. Kiselev
本文证明了微分方程− d2 u/dx 2 +V（x）u=Eu的解的WKB渐近性态，其中a.e.其中V=V1+V2，V1∈Lp（R），V2有界且A=lim supx→∞ V（x），而V′2（x）∈Lp（R），1 <$p<2。这些结果意味着具有这种势的Schrodinger算子在（A，∞）上具有绝对连续的谱.我们还建立了一些能量相关势函数解的WKB渐近性态。
We prove the WKB asymptotic behavior of solutions of the differential equation −d2u/dx2+V(x) u=Eu for a.e. E>A where V=V1+V2, V1∈Lp(R), and V2 is bounded from above with A=lim supx→∞ V(x), while V′2(x)∈Lp(R), 1⩽p<2. These results imply that Schrodinger operators with such potentials have absolutely continuous spectrum on (A, ∞). We also establish WKB asymptotic behavior of solutions for some energy-dependent potentials.