具有SU(1,1)李代数结构的广义谐振子系统精确求解  

Exact Solution of General Harmonic Oscillators Based on SU(1,1) Lie Algebraic Structures

作　　者：李伟 曹冰冰 郝刚领[1] LI Wei;CAO Bingbing;HAO Gangling(School of Physics and Electronic Information,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学物理与电子信息学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2022年第1期16-19,26,共5页Journal of Yan'an University：Natural Science Edition

基　　金：延安大学博士科研启动项目(YDBK2018-22);陕西省大学生创新创业训练计划项目(S202110719068)。

摘　　要：外场驱动下广义谐振子量子系统的动力学演化是实现诸如量子阱中离子的相干调控的重要途径。为了实现超快且高保真度的量子调控,一个重要的前提是对广义谐振子系统满足的薛定谔方程进行精确求解。文中利用代数动力学方法,通过选取适当的正则变换确定了两表象之间的对应关系,建立了可以解析求解的具有SU(1,1)李代数结构的广义谐振子系统的哈密顿量,进一步通过求解薛定谔方程,得到了系统波函数的解析表达式。本研究思路对具有其他半单李代数结构量子系统的动力学研究具有一定的借鉴意义。The dynamical evolution of a general harmonic oscillators quantum system,such as ions in quantum well,driven by external field is an important way to realize coherent quantum control.In order to achieve ultrafast and high fidelity quantum control,an important premise is to accurately solve the Schödinger equation.In this paper,by employing the algebraic dynamics method and adopting the desired canonical transformation,the corresponding relationship between the two representations is determined,the analytical expression of the external field of general harmonic oscillators with SU(1,1)Lie algebraic structure is obtained,and further the analytic expression of the wave function of the system is obtained by solving the Schödinger equation.The research has a certain reference significance for the dynamics of quantum systems with other quantum systems processing special semi simple Lie algebraic structures.

关 键 词：SU(1 1)李代数 广义谐振子系统 正则变换 精确解 

分 类 号：O413.1[理学—理论物理]