Stability of the absolutely continuous spectrum for multidimensional Schrödinger operators
Stability of the absolutely continuous spectrum for multidimensional Schrödinger operators
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多维薛定谔算子绝对连续谱的稳定性
DOI：
10.1155/imrn.2005.2289
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
G. Perelman
中科院分区：
文献类型：
--
作者：
G. Perelman
我们考虑L2（λ 3）中具有缓慢衰减势V的Schr dinger算子− λ +V，证明了这些算子的绝对连续谱本质上由λ +支撑，只要V满足|V（x）|+|X|| V ′（x）|≤C < x>−1/2−ε，ε>0，θ ′是梯度的角分量。
We consider the Schrödinger operators −▵+V in L2(ℝ3) with slowly decaying potentials V. We prove that the absolutely continuous spectrum of these operators is essentially supported by ℝ+provided V satisfies |V(x)|+|x||∇′ V(x)|≤C< x>−1/2−ε, ε>0, ∇′ being the angular component of the gradient.