两个耦合驱动谐振子精确的经典与量子动力学研究  

Study on exact classical and quantum dynamics of two coupled driven harmonic oscillators

作　　者：陈康康 李海凤 欧智敏 张凯峰 CHEN Kang-kang;LI Hai-feng;OU Zhi-min;ZHANG Kai-feng(School of Science,Xi’an Technological University,Xi’an,Shaanxi 710021,China)

机构地区：[1]西安工业大学基础学院物理系,陕西西安710021

出　　处：《大学物理》2024年第4期22-25,35,共5页College Physics

基　　金：国家自然科学基金(21703166);陕西省科技厅自然科学基础研究计划(2023-JC-QN-0151);西安工业大学研究生课程思政建设项目(XAGDYJ220511)资助。

摘　　要：谐振子模型作为一类可严格解析求解的体系,在物理学中占据重要地位,是描述许多物理过程非常有力的理论模型,而关于驱动谐振子的研究却较少涉及.本文研究了两个耦合驱动谐振子模型精确的经典与量子动力学.在经典力学框架下利用哈密顿正则方程给出含时驱动外场作用在两个耦合谐振子体系的精确能量值.在量子力学框架下考虑非含时驱动外场,给出系统的能量本征值和对应的本征态.考虑含时驱动外场,利用算子代数方法得到该量子体系t时刻的波函数和对应的能量期望值.由于在量子力学框架下微观粒子具有波粒二象性,因此两个驱动耦合谐振子体系的经典与量子动力学存在明显差异.The harmonic oscillator model,which can be analytically solved,takes an important part in physics and is a powerful theoretical model for describing many physical processes.However,the research on driven harmonic oscillator is rarely involved.In this paper,we study the exact classical and quantum dynamics of two coupled harmonic oscillators in the driving external fields.In the framework of classical mechanics,the exact energy values of the time-dependent external fields acting on two coupled harmonic oscillator systems are obtained by virtue of the Hamiltonian canonical equations.If the driven fields are constant,the energy eigenvalues and eigenstates of the system in quantum mechanics are attained.In consideration of the time-dependent driven fields,the expected energy values and wave function of quantum system are derived using operator algebra methods.Because the microscopic particles have wave-particle duality within the framework of quantum mechanics,there are obvious differences between the classical and quantum dynamics for the system consisted of the two coupled harmonic oscillators in the external driving fields.

关 键 词：两个耦合谐振子 含时驱动外场 经典动力学 量子动力学 

分 类 号：O411.1[理学—理论物理]