基于量子力学的相互作用绘景构造非线性哈密顿系统的数值计算方法  

Construction of Numerical Methods of Nonlinear Hamiltonian Systems Based on Interaction Picture of Quantum Mechanics

作　　者：张素英[1] 

机构地区：[1]山西大学理论物理研究所,山西太原030006

出　　处：《山西大学学报（自然科学版）》2012年第2期271-275,共5页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(10972125);高等学校博士学科点专项科研基金(20111401110004);山西省自然科学基金(2010011001-2);山西省留学回国人员科研基金

摘　　要：文章在量子力学的相互作用绘景中给出了非线性哈密顿系统离散格式的构造方法.首先将原非线性哈密顿问题变换至相互作用绘景,导出一个含时的常微分方程系统,离散该常微分方程并变换回原系统的态矢即可得到原问题的离散格式.基于不同的常微分方程数值方法,可得到原系统不同的离散格式.该方法还可以有效地求解多组分的Bose-Einstein凝聚态物理问题.Numerical methods of nonlinear Hamiltonian systems are constructed in the interaction picture of quantum mechanics.Firstly the original system is transformed to interaction picture of quantum mechanics.This reduces the problem to a system of ordinary differential equations in time.Subsequently,the modified system is integrated in time and then transformed back to the initial representation of the state vector.Varies discrete schemes can be obtained based on different integration methods.The methods in this paper can also be used to solve multi-component Bose-Einstein condensate problem.

关 键 词：偏微分方程 非线性哈密顿系统 BOSE-EINSTEIN凝聚体 

分 类 号：O469[理学—凝聚态物理]