求解自治非线性薛定谔方程的分离变量法  

A VARIABLE SEPARATION METHOD FOR SOLVING AUTONOMOUS NONLINEAR SCHRODINGER EQUATIONS

作　　者：刘燕[1] 张素英[1] 

机构地区：[1]山西大学理论物理研究所,太原030006

出　　处：《动力学与控制学报》2015年第6期401-405,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(91430109);高等学校博士学科点专项科研基金资助项目(20111401110004);山西省自然科学基金资助项目(201401100-3)~~

摘　　要：薛定谔方程是量子力学的基本方程,与经典物理中的牛顿运动方程地位相当.本文针对哈密顿量与时间无关的量子系统,应用分离变量法研究其量子力学定态解.分别给出了包含克尔型、饱和型以及五次非线性效应的薛定谔方程的定态解,并将所得解析解与数值解进行比较.两者完全吻合.The Schrodinger equations is a basic equation of quantum mechanics. It＇ s just as important as Newton＇ s equation of motion of classical physics in quantum mechanics. In this paper, we use variable separation method to obtain the stationary solution of the quantum mechanical system with time independent Hamihonian. We separately give solutions of Schrodinger equations with Kerr type, saturation type and quintic nonlinearity. And the obtained analytical solutions are compared with the numerical solutions. They agree well with each other.

关 键 词：非线性薛定谔方程 定态解 解析解 

分 类 号：O413.1[理学—理论物理]