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

Research output: Contribution to journalReview articleContributedpeer-review

Contributors

Abstract

In this review, we give a comprehensive comparison of the most widely used coherent state (CS) based methods to solve the time-dependent Schrodinger 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.

Details

Original languageEnglish
Pages (from-to)81-125
Number of pages45
JournalInternational reviews in physical chemistry
Volume40
Issue number1
Publication statusPublished - 2 Jan 2021
Peer-reviewedYes

External IDs

Scopus 85093092594

Keywords

Keywords

  • Coherent states, HERMAN-KLUK PROPAGATOR, INITIAL-VALUE REPRESENTATION, LONG-TIME, MATRIX, MECHANICS, MOTION, Morse oscillator, PHASE-SPACE, QUANTUM DYNAMICS, SEMICLASSICAL HYBRID APPROACH, Schrodinger equation, WAVE-PACKET DYNAMICS, variational principle