一维强场模型研究中的非齐线性正则方程的辛算法  

THE SYMPLECTIC METHOD FOR SOLVING THE LINEAR INHOMOGENEOUS CANONICAL EQUATIONS IN 1-DIMENSIONAL INTENSE FIELD MODEL

作　　者：刘晓艳[1] 刘学深[2] 周忠源[2] 丁培柱[2] 

机构地区：[1]东北师范大学数学系,吉林长春130024 [2]吉林大学原子与分子物理研究所,吉林长春130023

出　　处：《计算物理》2002年第1期62-66,共5页Chinese Journal of Computational Physics

基　　金：国家 973项目;自然科学基金 ( 197710 41;10 0 740 19)资助项目

摘　　要：就一维强场模型 ,采用对称差商代替空间变量的 2阶偏导数 ,将含有Schr dinger方程的初边值问题离散成“非齐线性正则方程” ,它的齐方程的通解和非齐方程特解都由“辛变换生成” ,分别采用辛格式计算 .采用这种辛算法和R K法计算了一个数值例子 ,并与精确解作了比较 .结果表明 ,经长时间计算后 ,辛算法保持解的固有特征 ,而RFor an intense field model, the time\|dependent Schrdinger equation with initial and boundary conditions can be discretized into the inhomogeneous linear canonical equation by substituting the symmetric difference quotient for the partial derivative. As the general solution of its homogeneous equation and the particular solution of the inhomogeneous equation can be generalized by the symplectic transformation, it is a reasonable numerical method to use the symplectic scheme. To prove its utility, a simple example is described using the symplectic scheme and RK method, and compared with the exact solution. The results show that the solution using the symplectic scheme can preserve the intrinsic properties of the equations after a long evolution, but RK method cannot. [

关 键 词：一维强场 非齐线性正则方程 辛格式 辛算法 原子 模型 SCHRODINGER方程 量子系统 

分 类 号：O562[理学—原子与分子物理] O413[理学—物理]