极坐标系下二维各向同性谐振子能级及波函数的研究  

Study on the Energy Levels and Wave Functions of Two-dimensional Isotropic Harmonic Oscillator in Polar Coordinate System

作　　者：孙晶 张海丰[1] SUN Jing;ZHANG Hai-feng(School of Science,Jiamusi University,Jianiusi Heilongjiang 154007,China)

机构地区：[1]佳木斯大学理学院,黑龙江佳木斯154007

出　　处：《佳木斯大学学报（自然科学版）》2020年第4期168-170,共3页Journal of Jiamusi University：Natural Science Edition

基　　金：黑龙江省省属本科高校基本科研业务费科研项目资助(2019-KYYWF-1363)。

摘　　要：利用代数解法研究了平面直角坐标系和平面极坐标系下二维各向同性谐振子的能级分布及本征波函数。结果表明在不同坐标系下,能级分布、简并度、宇称等物理量不变,只是本征波函数的表示形式发生了变化,同时在平面极坐标系二维各向同性谐振子的求解为进一步理解量子力学相关本征值问题的代数解法具有一定的理论意义。The energy level distribution and eigenwave function of two-dimensional isotropic harmonic oscillator in plane rectangular coordinate system and plane polar coordinate system are studied by algebraic solution method.Results show that under different coordinate system,energy distribution,degeneracy,parity and other physical quantities don′t change,only the representation of eigenwave function has changed.At the same time,to solve in order to further understand algebraic eigenvalue problem of the two-dimensional isotropic harmonic oscillator,the plane polar coordinates is presented has a certain theoretical significance.

关 键 词：代数解法 极坐标系 二维各向同性谐振子 能级分布 本征波函数 

分 类 号：O431[机械工程—光学工程]