含时受迫谐振子系统的求解

Solution of time-dependent driven harmonic oscillator system

含时受迫谐振子系统与许多实际物理问题有密切联系。用SU(1,1)李代数的方法求解了具有SU(1,1)+h(3)含时受迫谐振子的量子系统。首先求解哈密顿量H0(t)的时间演化算符,再求解相互作用V(t)的时间演化算符,最后得到系统总的时间演化算符。用一个实例证实了此方法的正确性。

Time-dependent driven harmonic oscillator system is closely related to many practical physical problems.SU(1,1)Lie algebra is used to solve the problem of SU(1,1)h(3)time-dependent forced harmonic oscillator system.Firstly,the time evolution operator of Hamilton H0(t)is solved,then the time evolution operator of V(t)in interaction representation is solved.Finally,the general time evolution operator of system is obtained.One example is given to demonstrate the correctness of the method.