广义振子量子相位和经典相位的新求解  

A New Way to Get the Quantum Phases and the Classical Phases of the Generalized Oscillator

作　　者：袁兵[1] 郭俊怀[2] 

机构地区：[1]天津大学理学院应用物理系,天津300072 [2]南开大学化学院,天津300071

出　　处：《辽宁大学学报（自然科学版）》2003年第3期212-214,共3页Journal of Liaoning University：Natural Sciences Edition

基　　金：天津大学教育振兴行动计划基金资助

摘　　要：采用试探函数法求解广义振子的薛定谔方程,结果表明广义振子的波函数是中心按照经典运动方程运动的波包.与此相应,广义振子的量子几何相位由两部分组成:一部分是由波包形状的改变引起的,另一部分则是由波包中心的运动引起的.进一步通过广义振子经典运动方程的精确解,得出了广义振子的经典相位,从而也得到了广义振子量子相位和经典相位的一般关系.Using the trial function method to solve the Schrondinger equation of the generalized harmonic oscillator shows that the wave functions are wave packets with the center following the classical equation of motion. Correspondingly, the quantum geometrical phase is divided into two parts; one part is produced by the shape change of the wave packet and the other is generated by the motion of the wave packet center. Further, through the exact solutions of the classical equation, the classical phase is derived and the general relation between the quantum phases and the classical phases is also achieved.

关 键 词：量子力学 广义振子 量子相位 经典相位 薛定谔方程 试探函数法 相干态 

分 类 号：O413.1[理学—理论物理]