Herman-Kluk算子的数学证明
A Mathematical Justification for the Herman-Kluk Propagator
摘要：
构造了一类在半经典极限$\eps\to 0$内收敛于Schroedinger方程酉群的Fourier积分算子.收敛是在统一的运营商规范，并允许一个错误界的顺序$O(\eps^{1-ρ})$为Escherichfest时间尺度，其中$ρ$可以任意小。对于O（1）阶的较短时间，$\eps$中的误差可以改进到任意阶。在化学文献中，这种近似被称为赫尔曼-克鲁克传播子。
英文摘要：
A class of Fourier Integral Operators which converge to the unitary group of the Schroedinger equation in semiclassical limit $\eps\to 0$ is constructed. The convergence is in the uniform operator norm and allows for an error bound of order $O(\eps^{1-ρ})$ for Ehrenfest timescales, where $ρ$ can be made arbitrary small. For the shorter times of order O(1), the error can be improved to arbitrary order in $\eps$. In the chemical literature the approximation is known as the Herman-Kluk propagator.
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