三体耦合摆量子系统的精确波函数  

Exact wave function of the three-body coupled pendulum quantnm 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11期7-9,13,共4页College Physics

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

摘　　要：利用不变本征算符法研究了三体耦合摆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.推导出在坐标表象中系统的精确波函数的解析解.但是,不变本征算符法对于计算系统哈密顿量中包含力学量的3次方及3次方以上的项时非常复杂.The normal frequencies and its corresponding normal coordinates and conjugate momentums for a three-body coupled pendulum quantum system is derived in terms of the invariant eigen-operator method. With Hamiltonian of the system decoupled, the visible analytic solutions of normal frequencies in the system are obtained. The analytic solutions of exact wave function of the system in coordinate representation are deduced. Whereas, when calculating the Hamiltonian containing mechanical quantity with invariant eigen-operator method, the three power and more than three power terms of system Hamihonian are very intricacy.

关 键 词：不变本征算符法 耦合摆量子系统 简正频率 精确波函数的解析解 

分 类 号：O413.1[理学—理论物理]