{"title":"Multiresolution of the one dimensional free-particle propagator. Part 2: Implementation","authors":"Evgueni Dinvay","doi":"10.1016/j.cpc.2024.109438","DOIUrl":null,"url":null,"abstract":"<div><div>A novel method to integrate the time-dependent Schrödinger equation within the framework of multiresolution analysis is presented. The method is based on symplectic splitting algorithms to separate the kinetic and potential parts of the corresponding propagator. The semigroup associated with the free-particle Schrödinger operator is represented in a multiwavelet basis. The propagator is effectively discretised with a contour deformation technique, which overcomes the challenges presented by previous discretisation methods. The discretised operator is then employed in simple numerical simulations to test the validity of the implementation and to benchmark its precision.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"308 ","pages":"Article 109438"},"PeriodicalIF":3.4000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465524003618","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/11/19 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
A novel method to integrate the time-dependent Schrödinger equation within the framework of multiresolution analysis is presented. The method is based on symplectic splitting algorithms to separate the kinetic and potential parts of the corresponding propagator. The semigroup associated with the free-particle Schrödinger operator is represented in a multiwavelet basis. The propagator is effectively discretised with a contour deformation technique, which overcomes the challenges presented by previous discretisation methods. The discretised operator is then employed in simple numerical simulations to test the validity of the implementation and to benchmark its precision.
期刊介绍：
The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper.
Computer Programs in Physics (CPiP)
These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged.
Computational Physics Papers (CP)
These are research papers in, but are not limited to, the following themes across computational physics and related disciplines.
mathematical and numerical methods and algorithms;
computational models including those associated with the design, control and analysis of experiments; and
algebraic computation.
Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.
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