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.
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.