麦克斯韦分布的数学处理

本文从数学处理的角度对麦克斯韦分布作了较详细的讨论,同时着重于对于物理概念的阐明。首先给出一种比较简洁的麦氏分布导出方法,强调指出了在导出麦氏分布时所使用的假定。然后,依次讨论在一维、二维、三维速度空间中麦氏速度与速率分布的不同形式的公式、图象,同时指出如何利用误差函数、高斯正态分布函数的图表把麦氏分布公式简化,而便于数据处理应用。本文不仅在概念上而且在公式上都明确地指出了麦氏分布中速度分布与速率分布的区别联系,最后给出了用各种方法计算麦氏分布问题的实例。

THE MATHEMATICAL TREATMENT OF THE MAXWALL DISTRIBUTION

In this paper, the Maxwell distribution has been discussed in detail in mathematical treatment, especially, the physical conception is emphasized. First of all, a simple methed of derivation of the Maxwell distridution is put forward, and the asumptions used in the derivation of Maxwell distribution are also stressed. Then the distribution′s formulas and diagrams in one-demension, two-demension and three-demension are discussed in turn. At the same time, it has pointed out how to simplify the Maxwell distribution by using erf(x) and Gaussian distribution, and to be convenient for dealing with data and applying. The thesis tells the difference between the speed distribution and rate distribution clearly not only in concept, but also in formulas. At last, some examples of various caculations in the Maxwell distribution have been presented.