三维各向同性谐振子的代数解法  

Algebraic solution of 3-dimensional isotropic harmonic oscillator

作　　者：李兴华[1] 杨亚天[1] 

机构地区：[1]福建师范大学物理系,福建福州350007

出　　处：《大学物理》2003年第5期17-21,共5页College Physics

基　　金：国家自然科学基金资助项目 ( 193 75 0 12 );福建省教委资助项目 (k2 0 0 10 41)

摘　　要：用带角动量的玻色算子统一构成三维各向同性谐振子的能量本征函数 ,并讨论了它们和直接求解微分方程得到的本征解之间的关系 .这种方法快捷优美 。By using the boson operators which carry angular momentum of one unit the eigenfunctions of hamiltonian of 3-dimensional isotropic harmonic oscillator are constructed uniformly. The relation between algebraic solution and the solution obtained by solving differential equation directly are discussed. The method is simple and elegant. We have a unified expression for eigenstates here. The Lie algebra between the operators used are quite simple.

关 键 词：三维各向同性谐振子 代数解法 角动量 玻色算子 能量本征函数 李代数关系 量子力学 

分 类 号：O413.1[理学—理论物理] O411[理学—物理]