布朗运动的定量分析与讨论

Quantitative Analysis and Discussion on Brownian Motion

布朗运动是热学教学中气体动理论的重要内容,大多数教材将布朗运动作为分子热运动的引入部分。该研究通过求解朗之万方程给出布朗粒子速度和位置的统计规律,以及速度和位置的分布函数,从而定量讨论布朗粒子的扩散现象。布朗运动的讨论有助于学生对气体动理论以及统计理论的深入理解。

Brownian motion is an important part of gas kinetic theory in the teaching of thermal physics. In most of textbooks, Brownian motion is the introduction of molecular thermal motion. By solving the Langevin equation, the statistical laws of the velocity and position of Brownian particles, as well as the distribution functions of the velocity and position, are given in this paper, so that the diffusion phenomenon of Brownian motion is quantified. The discussion of Brownian motion is helpful for students to understand the theory of gas dynamics and statistical theory.