用摄动配置方法求解含时薛定谔方程

SOLVING TIME-DEPENDENT SCHRDINGER EQUATIONS WITH PERTURBED COLLOCATION METHOD

将摄动配置方法应用到含时薛定谔方程,在计算实现的基础上结合摄动配置的特征提出了一类新的数值积分方法,并给出了一个2级2阶和一个3级4阶的辛摄动配置方法对含时薛定谔方程的数值算例.为了检验新的数值积分方法,我们还给出了与两个辛摄动配置格式在理论上等价的辛龙格.库塔方法以及同阶的非辛方法的数值模拟.展示了一些数值结果,并给出了一些分析.

The so-called perturbed collocation method is used to the time-dependent SchrSdinger equation and a novel kind of numerical integration based on the computational realization is proposed. A 2-stage 2-order and a 3-stage 4-order symplectic perturbed collocation methods are constructed and used to simulate this SchrSdinger equation numerically. The numerical experiments by using the two equivalent symplectic Runge-Kutta methods and two non-symplectic methods of the same order show that the new numerical integration method is effective.