Coherent state based solutions of the time-dependent Schrödinger equation: hierarchy of approximations to the variational principle

IF 2.5 2区 化学 Q3 CHEMISTRY, PHYSICAL
Michael Werther, Sreeja Loho Choudhury, F. Grossmann
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引用次数: 18

Abstract

In this review, we give a comprehensive comparison of the most widely used coherent state (CS) based methods to solve the time-dependent Schrödinger equation (TDSE). Starting from the fully variational coherent states (VCS) method, after a first approximation, the coupled coherent states (CCS) method can be derived, whereas an additional approximation leads to the semiclassical Herman–Kluk (HK) method. We numerically compare the different methods with another one, based on a static rectangular grid of coherent states (SCS), by applying all of them to the revival dynamics in a 1D Morse oscillator, with a special focus on the number of basis states (for the CCS and HK methods the number of classical trajectories) needed for convergence and the related issue of tight frames, which in principle allow the usage of CSs as if they were orthogonal. Different discretisation strategies for the occurring phase space integrals for systems with more degrees of freedom are also discussed and the apoptosis procedure that allows to circumvent the linear dependency problem in the VCS method is reviewed. The Holstein molecular crystal model serves to further illustrate the latter point.
时间相关Schrödinger方程的相干状态解:变分原理的近似层次
在这篇综述中,我们给出了最广泛使用的基于相干态(CS)的方法来解决时间相关Schrödinger方程(TDSE)的全面比较。从全变分相干态(VCS)方法出发,经过一次近似,可以推导出耦合相干态(CCS)方法,而再进行一次近似则可以推导出半经典的Herman-Kluk (HK)方法。我们将不同的方法与另一种方法进行数值比较,基于静态矩形相干态网格(SCS),通过将所有方法应用于一维莫尔斯振荡器的恢复动力学,特别关注收敛所需的基态数量(对于CCS和HK方法,经典轨迹的数量)和紧密框架的相关问题,原则上允许使用CSs,就好像它们是正交的一样。还讨论了对具有更多自由度的系统的相空间积分的不同离散化策略,并回顾了在VCS方法中允许规避线性依赖问题的细胞凋亡过程。荷尔斯坦分子晶体模型进一步说明了后一点。
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来源期刊
CiteScore
14.20
自引率
1.60%
发文量
5
审稿时长
1 months
期刊介绍: International Reviews in Physical Chemistry publishes review articles describing frontier research areas in physical chemistry. Internationally renowned scientists describe their own research in the wider context of the field. The articles are of interest not only to specialists but also to those wishing to read general and authoritative accounts of recent developments in physical chemistry, chemical physics and theoretical chemistry. The journal appeals to research workers, lecturers and research students alike.
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