一维谐振子低能量子态的数值求解及其动力学模拟  

Numerical solution and dynamic simulation of low energy quantum states of one-dimensional harmonic oscillator

作　　者：江迅达 刘彬 黎永耀[1,2] 秦锡洲 JIANG Xun-da;LIU Bin;LI Yong-yao;QIN Xi-zhou(School of Physics and Optoelectronic Engineering,Foshan University,Foshan 528225,China;Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology,Foshan 528225,China)

机构地区：[1]佛山科学技术学院物理与光电工程学院,广东佛山528225 [2]佛山科学技术学院粤港澳智能微纳光电技术联合实验室,广东佛山528225

出　　处：《佛山科学技术学院学报（自然科学版）》2023年第3期27-31,共5页Journal of Foshan University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11904051);广东省基础与应用基础研究基金资助项目(2021A1515111015);广东省自然科学基金资助项目(2021A1515010214);粤港澳智能微纳光电技术联合实验室资助项目(2020B1212030010)。

摘　　要：以一维谐振子为例,详细地介绍了虚时间传播法求解基态和低能激发态的原理过程,利用虚时间传播法数值求解出体系的基态和低能激发态解,并与精确解比较,验证虚时间传播法求解激发态的准确性。另一方面,展示了谐振子基态自由扩散、谐振运动和碰撞等动力学过程及特性。研究结果很好地将虚时间传播法推广到了求解体系的激发态。Take the one-dimensional harmonic oscillator as an example,the procedure of ITPM to find the ground and low-energy excited states is presented in detail.We numerically obtain the ground state and low energy excited state solutions of the system using the ITPM,and compare the results with the exact ones in order to verify the accuracy of the ITPM for excited states.Moreover,the quantum dynamics,such as ground-state free expansion,oscillation motion and collision of harmonic oscillators are shown vividly.Finally,our results show the feasibility of applying ITPM to excited states of a quantum system.

关 键 词：量子谐振子 虚时间 量子态 动力学 

分 类 号：O413[理学—理论物理]