两体量子模型的代数动力学方法求解  

USING ALGEBRAIC DYNAMICS METHOD TO SOLUTE TWO-MODE QUANTUM SYSTEM

作　　者：张新琴[1] 夏秀文[1] 罗小兵[1] 

机构地区：[1]井冈山大学数理学院,江西吉安343009

出　　处：《井冈山大学学报（自然科学版）》2013年第2期28-31,共4页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(10965001)

摘　　要：引入广义坐标和广义动量,将非线性自洽两体量子模型表述为经典不含时哈密顿系统并实现了去约束经典哈密顿量的正则化。量子系统的整体规范不变性,体现在去约束经典哈密顿量和哈密顿动力学关系的不变性中。利用代数动力学方法求解经典哈密顿方程,得到了两体量子系统的六阶近似分析解。As it well known, quantum system can be translated to classic Hamilton system strictly by using generalized coordinate and generalized momentum. Furthermore, we deal with a nonlinear self-consistent two-mode quantum system which shows that the Schrodinger equations can be described as classic Hamilton equations. Furthermore, the classic Hamiltonian and the Hamilton equations kept unchanged during gauge transformation. Taken advantage of algebraic dynamics, the quantum system can be solved analytically in 6th order.

关 键 词：非线性自洽量子系统 正则变换 哈密顿量 代数动力学 

分 类 号：O413.1[理学—理论物理]