摘要
利用有限元方法求解单粒子在多角形势阱中的能量以及概率密度.分别用差分方法和有限元方法进行数值仿真,将这两种方法求得的数值结果和解析解分别对比.结果表明差分方法的求解误差更小,但是在误差允许的范围内,有限元方法能适用于更多不同势阱形状的求解.对于高精度地求解薛定谔方程的数值解开辟了新道路,丰富了对量子现象的研究手段.
People are familiar with the probability density distribution of a single particle in a square potential well,but there are few visual images of the probability density distribution of particles in a polygonal potential well.In this paper,the energy and probability density of a single particle in a polygonal potential well are solved by the finite element method.The difference method and finite element method are used for numerical simulation,and the numerical results obtained by these two methods are compared respectively with the analytical solutions.The results show that the error of the difference method is smaller,but the finite element method can be applied to solve more different potential well shapes within the allowable range of error.This paper opens up a new way for solving Schrodinger’s numerical solution with high precision,and enriches the means of studying quantum phenomena.
作者
魏健达
张江敏
WEI Jianda;ZHANG Jiangmin(College of Physics and Energy,Fujian Normal University,Fuzhou 350117,China)
出处
《福建师范大学学报（自然科学版）》
CAS
2022年第1期24-33,共10页
Journal of Fujian Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(11704070)。
关键词
二维势阱
薛定谔方程
有限元方法
差分法
雅可比矩阵
two-dimensional potential well
Schrodinger equation
finite element method
difference method
Jacobian matrix
