质量和频率随时间变化的受迫谐振子的传播子

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夏小建( 1966—) ，男，福建长汀人，泉州师范学院物理信息学院副教授，硕士，主要从事大学物理教学

收稿日期: 2018-01-07

修回日期: 2018-06-12

网络出版日期: 2019-03-01

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Propagator of the driven oscillator with time-dependent mass and frequency

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School of Physics and Information Engineering，Quanzhou Normal College，Quanzhou，Fujian 362000，China

Received date: 2018-01-07

Revised date: 2018-06-12

Online published: 2019-03-01

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质量和频率随时间变化的谐振子可描述许多物理系统，研究和求解含时系统在量子场论和量子光学中有重要的意

义.本文用SU( 1，1) 李代数的方法求解了质量和频率随时间变化的谐振子系统.通过求解黎卡提方程，得到系统算符的系数.在

相空间推导了体系传播子的计算公式.最后，计算了自由粒子、受重力场驱动、质量随周期变化和阻尼谐振子的传播子.

关键词： 传播子; 受迫谐振子; SU( 1; 1) 李代数; 黎卡提方程

夏小建, 陈文志 . 质量和频率随时间变化的受迫谐振子的传播子[J]. 大学物理, 2019 , 38(1) : 32 . DOI: 10.16854 /j.cnki.1000-0712.180024

Many physical systems can be described by oscillator with time-dependent mass and frequency. Investigation

and solution of time-dependent system are very important in quantum field as well as in quantum optics.

We use SU( 1，1) Lie-algebraic technique to investigate the harmonic oscillator with time-dependent mass and frequency

and obtain the time evolution operator by solving Riccati equation. Than the formula of the system is derived

in phase space. Finally，we obtain the propagator of oscillator of the free particle，driven by gravity，period mass

　　and damped system.

Key words： forced oscillator; Riccati equation; SU( 1; 1) Lie-algebraic; propagator

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