TY - JOUR
T1 - Novel Conservative Methods for Schrödinger Equations with Variable Coefficients over Long Time
AU - Xu Qian, Yaming Chen & Songhe Song
JO - Communications in Computational Physics
VL - 3
SP - 692
EP - 711
PY - 2014
DA - 2014/03
SN - 15
DO - http://doi.org/10.4208/cicp.120313.020813a
UR - https://global-sci.org/intro/article_detail/cicp/7111.html
KW - 
AB - <p style="text-align: justify;">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 Schrödinger 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.</p>