求解时变薛定谔方程的辛伪谱时域格式

IF 0.7 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC

Progress in Electromagnetics Research M Pub Date : 2018-05-08 DOI:10.2528/PIERM18010808

Jing Shen, W. Sha, Xiaojing Kuang, Jinhua Hu, Zhixiang Huang, Xianliang Wu

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引用次数: 0

摘要

提出了一种求解薛定谔方程的辛伪谱时域格式。利用快速傅里叶变换代替传统时域有限差分法中的空间有限差分来计算空间导数。在时域上，采用高阶辛积分器模拟薛定谔方程的时间演化。对一维量子阱和三维谐振子的特征值问题进行了详细的数值研究。仿真结果有力地验证了SPSTD方案相对于传统PSTD方法和FDTD方法的优越性。通过与传统的PSTD方法和RK方法的比较，表明SPSTD格式在空间上具有无限阶精度，在时间上具有节能性，适合于长期仿真。

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Symplectic Pseudospectral Time-Domain Scheme for Solving Time-Dependent Schrodinger Equation

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.

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来源期刊

Progress in Electromagnetics Research M Materials Science-Electronic, Optical and Magnetic Materials

CiteScore

2.50

自引率

10.00%

发文量

114

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.