n模耦合谐振子量子系统的精确波函数  

Exact wave function of the n-module coupled harmonic oscillators quantum system

作　　者：成泰民[1] 孙立红[1] 

机构地区：[1]沈阳化工大学数理系,辽宁沈阳110142

出　　处：《大学物理》2011年第9期10-14,共5页College Physics

基　　金：国家自然科学基金(10647138);辽宁省教育厅科学研究项目(20060667)资助课题

摘　　要：利用不变本征算符法研究了n模耦合谐振子量子系统的简正频率及其对应的简正坐标与共轭动量,并对系统的哈密顿量进行了退耦合,得到了系统的明显的简正频率解析解.推导出坐标表象中系统的精确波函数的解析解.并对不同情形的耦合系数进行了讨论,认识到n模动量耦合谐振子体系和n模坐标耦合谐振子体系是本文所研究的体系的特例.The normal frequencies and its corresponding normal coordinates and conjugate momentums of the n-module coupled harmonic oscillators quantum system are derived by using the invariant eigen-operator method.The Hamiltonian of the system is decoupled and then the visible analytic solution of normal frequencies in the system is obtained.The analytic solution of wave function of the system in the coordinate representation is deduced.Through the discussion of the coupling coefficients of different situations,we have concluded that the coupled harmonic oscillator systems with the n-module momentum or coordinates are just special cases of the system under study.

关 键 词：不变本征算符法 简正频率 n模耦合谐振子量子系统 精确波函数的解析解 

分 类 号：O413.1[理学—理论物理]