Semiclassical Dynamics¶with Exponentially Small Error Estimates
Semiclassical Dynamics¶with Exponentially Small Error Estimates
复制标题
具有指数小误差估计的半经典动力学¶
DOI：
10.1007/s002200050732
复制
发表时间：
1998
影响因子：
2.4
通讯作者：
A. Joye
中科院分区：
文献类型：
--
作者：
G. Hagedorn;A. Joye
摘要：
我们构造了含时薛定谔方程的近似解
对于较小的ħ值。如果V满足适当的解析性和增长假设，并且这些解与精确解一致，直到误差，其范数对于某些C和γ>；0是有界的。在更具限制性的假设下，我们证明了对于足够小的T‘，蕴含误差范数对某些C’，γ‘>；0和σ>；0是有界的。
Abstract:
We construct approximate solutions to the time–dependent Schrödinger¶equation
for small values of ħ. If V satisfies appropriate analyticity and growth hypotheses and , these solutions agree with exact solutions up to errors whose norms are bounded by for some C and γ>0. Under more restrictive hypotheses, we prove that for sufficiently small T′, implies the norms of the errors are bounded by for some C′, γ′>0, and σ > 0.