Time-decay of scattering solutions and resolvent estimates for semiclassical Schrödinger operators
Time-decay of scattering solutions and resolvent estimates for semiclassical Schrödinger operators
复制标题
半经典薛定谔算子的散射解的时间衰减和解析估计
DOI：
10.1016/0022-0396(88)90032-0
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发表时间：
1988
影响因子：
2.4
通讯作者：
Xue
中科院分区：
文献类型：
--
作者：
Xue
我们研究了半经典薛定谔算子−h2Δ+V（x），h <$0，1]，并建立了散射解的时间衰减和预解式幂的半经典界的各种结果。对于短程势，本文所得到的时间衰减结果是最好的，这使我们能够得出经典力学中的非俘获条件与量子力学中的波函数的一致时间衰减之间的等价性。
We study the semiclassical Schrödinger operator, −h2Δ+V(x),hϵ]0, 1], and establish various results on the time-decay of scattering solutions and the semiclassical bounds for the powers of the resolvent. For short range potentials, the time-decay results obtained in this paper are the best possible and this enables us to conclude the equivalence between the non-trapping condition in classical mechanics and the uniform time-decay of wave functions in quantum mechanics.