{"title":"Symplectic Pseudospectral Time-Domain Scheme for Solving Time-Dependent Schrodinger Equation","authors":"Jing Shen, W. Sha, Xiaojing Kuang, Jinhua Hu, Zhixiang Huang, Xianliang Wu","doi":"10.2528/PIERM18010808","DOIUrl":null,"url":null,"abstract":"A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schrodinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) method, the fast Fourier transform is used to calculate the spatial derivatives. In time domain, the scheme adopts high-order symplectic integrators to simulate time evolution of Schrodinger equation. A detailed numerical study on the eigenvalue problems of 1D quantum well and 3D harmonic oscillator is carried out. The simulation results strongly confirm the advantages of the SPSTD scheme over the traditional PSTD method and FDTD approach. Furthermore, by comparing to the traditional PSTD method and the non-symplectic Runge-Kutta (RK) method, the explicit SPSTD scheme which is an infinite order of accuracy in space domain and energy-conserving in time domain, is well suited for a long-term simulation.","PeriodicalId":39028,"journal":{"name":"Progress in Electromagnetics Research M","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2018-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2528/PIERM18010808","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress in Electromagnetics Research M","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2528/PIERM18010808","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schrodinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) method, the fast Fourier transform is used to calculate the spatial derivatives. In time domain, the scheme adopts high-order symplectic integrators to simulate time evolution of Schrodinger equation. A detailed numerical study on the eigenvalue problems of 1D quantum well and 3D harmonic oscillator is carried out. The simulation results strongly confirm the advantages of the SPSTD scheme over the traditional PSTD method and FDTD approach. Furthermore, by comparing to the traditional PSTD method and the non-symplectic Runge-Kutta (RK) method, the explicit SPSTD scheme which is an infinite order of accuracy in space domain and energy-conserving in time domain, is well suited for a long-term simulation.
期刊介绍:
Progress In Electromagnetics Research (PIER) M publishes peer-reviewed original and comprehensive articles on all aspects of electromagnetic theory and applications. Especially, PIER M publishes papers on method of electromagnetics, and other topics on electromagnetic theory. It is an open access, on-line journal in 2008, and freely accessible to all readers via the Internet. Manuscripts submitted to PIER M must not have been submitted simultaneously to other journals.