The semiclassically scaled time-dependent multi-particle Schrödinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This paper reviews and studies numerical approaches that are robust to the small semiclassical parameter. We present and analyse variationally evolving Gaussian wave packets, Hagedorn’s semiclassical wave packets, continuous superpositions of both thawed and frozen Gaussians, and Wigner function approaches to the direct computation of expectation values of observables. Making good use of classical mechanics is essential for all these approaches. The arising aspects of time integration and high-dimensional quadrature are also discussed.

中文翻译：

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计算半经典状态下的量子动力学

半经典尺度的时间相关多粒子薛定谔方程描述，除其他外，分子中原子核的量子动力学。它提出了高振荡和高维度的综合计算挑战。本文回顾和研究了对小半经典参数具有鲁棒性的数值方法。我们提出并分析了变分演化的高斯波包、Hagedorn 的半经典波包、解冻和冻结高斯的连续叠加，以及直接计算可观测值期望值的 Wigner 函数方法。充分利用经典力学对于所有这些方法都是必不可少的。还讨论了时间积分和高维求积的新兴方面。