量子力学中的哈密顿量理论及其应用  

Theory and Application of Hamiltonian in Quantum Mechanics

作　　者：潘桂侠 Pan Guixia(School of Mechanics and Optoelectronic Physics,Anhui University of Science and Technology,Huainan City,Anhui Province 232001)

机构地区：[1]安徽理工大学力学与光电物理学院,安徽淮南232001

出　　处：《黄河科技学院学报》2022年第11期1-5,共5页Journal of Huanghe S&T College

基　　金：安徽理工大学人才引进基金项目“耦合动腔中连续变量纠缠的理论研究”(11784);安徽省高校自然科学研究重点项目“带电腔光机械系统纠缠及其操控的理论研究”(KJ2020A0331);安徽省教育厅质量工程项目“安徽理工大学大学物理教学团队”(2019jxtd046)。

摘　　要：薛定谔方程中的哈密顿量是量子力学中最重要的力学量之一,其在宏观系统中的具体形式可用来研究量子效应。以耦合腔光机械系统中的量子纠缠和带电腔光机械系统中电磁诱导透明理论研究为典型案例,深度介绍哈密顿量的理论应用。同时,利用量子朗之万方程、Matlab应用软件进行数值计算,形成耦合腔光机械系统的纠缠图和带电腔光机械系统的电磁诱导透明图。The Hamiltonian of the Schrodinger equation is one of the most important mechanical quantities in quantum mechanics,and its specific form in macroscopic systems can be used to study the quantum effects of macroscopic systems.Taking quantum entanglement in coupled cavity optomechanical systems and the theoretical study of electromagnetically induced transparency in charged cavity optomechanical systems as typical cases,the theoretical application of Hamiltonian is introduced in depth.At the same time,the quantum Langevin equation and Matlab software are used for numerical calculation to form the entanglement diagram of the coupled cavity optomechanical system and the electromagnetically induced transparency diagram of the charged optomechanical system.

关 键 词：哈密顿量 薛定谔方程 量子朗之万方程 量子纠缠 电磁诱导透明 

分 类 号：O437[机械工程—光学工程]