We study the time-sliced thawed Gaussian propagation method, which was recently proposed for solving the time-dependent Schr\"odinger equation. We introduce a triplet of quadrature-based analysis, synthesis and re-initialization operators to give a rigorous mathematical formulation of the method. Further, we derive a combined error representation for the discretization of the wave packet transform and the time-propagation of the thawed Gaussian basis functions. Numerical experiments in 1D illustrate the theoretical results.
翻译:我们研究了时间剪切的高斯传播方法,这是最近为解决基于时间的 Schr\'odinger 等式而提出的。我们引入了三组基于二次等离子分析、合成和重新初始化的操作器,以给该方法提供严格的数学配方。此外,我们得出了波包变异的离散化和对时间转换高斯基函数的换代的合并错误表示。1D中的数值实验说明了理论结果。