一维谐振子的量子蒙特卡罗模拟  

Quantum Monte-Carlo simulation of one-dimensional harmonic oscillator

作　　者：刘鹏程[1] 傅俞钧 孙俊松 朱兴川 郭怀明 LIU Peng-cheng;FU Yu-jun;SUN Jun-song;ZHU Xing-chuan;GUO Huai-Ming(School of Physics,Beihang University,Beijing 102206,China;Interdisciplinary Center for Fundamental and Frontier Sciences,Nanjing University of Science and Technology,Jiangyin,Jiangsu 214443,China)

机构地区：[1]北京航空航天大学物理学院,北京102206 [2]南京理工大学基础前沿交叉中心,江苏江阴214443

出　　处：《大学物理》2024年第12期53-56,共4页College Physics

基　　金：国家自然科学基金(12074022)资助。

摘　　要：一维谐振子是量子力学中的一个重要模型.本文介绍了解决谐振子问题的量子蒙特卡洛模拟方法,推导了配分函数的路径积分公式,并使用量子蒙特卡洛方法计算了一维谐振子在有限温度下的能量、位置、动量、位置平方和动量平方等物理量,得到了与解析解一致的结果.本研究有助于学生加深对量子力学的理解,并且是Holstein电声子模型的量子蒙特卡洛数值模拟的基础,从而有助于开展相关科学研究.A one-dimensional harmonic oscillator is an important model in quantum mechanics.This paper introduces a quantum Monte-Carlo simulation method to solve the harmonic oscillator problem.We derive the path integral formula for the partition function and use quantum Monte-Carlo methods to calculate physical quantities such as energy,position,momentum,position squared,and momentum squared of a one-dimensional harmonic oscillator at finite temperature.The results obtained are consistent with analytical solutions.This study aids students in deepening their understanding of quantum mechanics and serves as the foundation for quantum Monte-Carlo numerical simulations of the Holstein electron-phonon model,thus facilitating related scientific research.

关 键 词：一维谐振子 量子蒙特卡罗方法 量子统计 

分 类 号：O411.3[理学—理论物理]