Novel Conservative Methods for Schrodinger Equations with Variable Coefficients over Long Time

作者：Qian, Xu^*; Chen, Yaming; Song, Songhe

来源：Communications in Computational Physics, 2014, 15(3): 692-711.

DOI：10.4208/cicp.120313.020813a

• Schrodinger equation
• wavelet collocation method
• splitting technique
• conservative property

In this paper, we propose a wavelet collocation splitting (WCS) method, and a Fourier pseudospectral splitting (FPSS) method as comparison, for solving one-dimensional and two-dimensional Schrodinger equations with variable coefficients in quantum mechanics. The two methods can preserve the intrinsic properties of original problems as much as possible. The splitting technique increases the computational efficiency. Meanwhile, the error estimation and some conservative properties are investigated. It is proved to preserve the charge conservation exactly. The global energy and momentum conservation laws can be preserved under several conditions. Numerical experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis.

• 出版日期2014-3
• 单位中国人民解放军国防科学技术大学