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.