求解三模耦合谐振子精确能谱的一种方法  

An approach to solve the exact energy spectrums of three-dimensional coupled harmonic oscillators

作　　者：王帅[1] 徐世民[1] 李洪奇[1] 

机构地区：[1]菏泽学院物理系,山东菏泽274015

出　　处：《大学物理》2010年第1期36-38,56,共4页College Physics

基　　金：山东省自然科学基金资助项目(Y2008A16);菏泽学院自然科学基金资助项目(XY09WL01)

摘　　要：基于相空间中的幺正转动变换,利用有序算符内的积分技术,得到了相空间中转动算符、傅里叶变换算符和宇称算符的相干态表示.进而引入并利用相空间中的三模转动算符,简捷地实现了三模坐标-动量耦合谐振子哈密顿量的退耦合,给出了该耦合形式谐振子的精确能谱及其能量本征态.Based on the rotation transformation in the phase space and the technique of integration within an ordered product of operators, the coherent state representations of the rotation operator in quantum phase space, the Fourier transform operator and the parity operator are derived. Then the three-mode rotation operator is introduced.By the three-mode rotation operator, the Hamilton of the three-dimensional coordinate-momentum coupled harmonic oscillators is simply decoupled. Then its exact energy spectrums and eigenstates are obtained.

关 键 词：转动算符 耦合谐振子 能谱 能量本征态 

分 类 号：O413.1[理学—理论物理]