Novel Conservative Methods for Schrödinger Equations with Variable Coefficients over Long Time (Communications in Computational Physics, 2014)
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 inquantum mechanics. The two methods can preserve the intrinsic properties of originalproblems 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 andmomentum conservation laws can be preserved under several conditions. Numericalexperiments are conducted during long time computations to show the performancesof the proposed methods and verify the theoretical analysis.