关键词: 薛定谔方程, 分裂法, 小波分析

Abstract: The paper presents a time-splitting and wavelet based space-time adaptive method for numerical solution of Schrodinger equat ions (the Planck constant ε is small). The multiresolution structure of wavelet orthonormal bases provides an adaptive way to the local regularity of the solution. In order to gain the stability and precision of the numerical scheme, we introduce an approximate sheme that adapt the time steps to the spatial resolution. Furthermore, numerical tests are presented.

Key words: Schrodinger equation, splitting method, wavele