Volume 15, Issue 3
Novel Conservative Methods for Schrödinger Equations with Variable Coefficients Over Long Time

Xu Qian, Yaming Chen & Songhe Song

Commun. Comput. Phys., 15 (2014), pp. 692-711.

Published online: 2014-03

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  • Abstract

In this paper, we propose a wavelet collocation splitting (WCS) method, and a Fourier pseudospectral splitting (FPSS) method as comparison, for solving onedimensional and two-dimensional Schr ¨odinger 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.

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@Article{CiCP-15-692, author = {}, title = {Novel Conservative Methods for Schrödinger Equations with Variable Coefficients Over Long Time}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {3}, pages = {692--711}, abstract = {

In this paper, we propose a wavelet collocation splitting (WCS) method, and a Fourier pseudospectral splitting (FPSS) method as comparison, for solving onedimensional and two-dimensional Schr ¨odinger 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120313.020813a}, url = {http://global-sci.org/intro/article_detail/cicp/7111.html} }
TY - JOUR T1 - Novel Conservative Methods for Schrödinger Equations with Variable Coefficients Over Long Time JO - Communications in Computational Physics VL - 3 SP - 692 EP - 711 PY - 2014 DA - 2014/03 SN - 15 DO - http://dor.org/10.4208/cicp.120313.020813a UR - https://global-sci.org/intro/article_detail/cicp/7111.html KW - AB -

In this paper, we propose a wavelet collocation splitting (WCS) method, and a Fourier pseudospectral splitting (FPSS) method as comparison, for solving onedimensional and two-dimensional Schr ¨odinger 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.

Xu Qian, Yaming Chen & Songhe Song. (2020). Novel Conservative Methods for Schrödinger Equations with Variable Coefficients Over Long Time. Communications in Computational Physics. 15 (3). 692-711. doi:10.4208/cicp.120313.020813a
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