可分线性哈密顿系统显式辛格式的守恒量

CONSERVATION QUANTITIES OF THE EXPLICIT SYMPLECTIC SCHEMES FOR SEPARABLE AND LINEAR HAMILTONIAN SYSTEMS

摘要: 证明了对可分线性哈密顿系统的每个二次形守恒量,1阶和2阶显式辛格式存在对应的格式守恒量;由此可说明,步长适当小时,1阶和2阶显式辛格式保持量子系统的波函数模方守恒,是直接求解时间相关Schrdinger方程(TDSE),以研究量子系统时间演化的合理和有效的数值方法。

Abstract: The scheme-conservation quantities of the 1-and 2-order explicit symplectic schemes are found according to the quadric-form conservation quantities for Separable and linear Hamiltonian Systems.It can be shown that so long as the time-step is properly small the norm and the energy can keep conservied in certain accuracy.