关键词: 一维谐振子, 量子蒙特卡罗方法, 量子统计

Abstract: 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.

Key words: onedimensional harmonic oscillator, quantum Monte-Carlo method, quantum Statistics