期刊名称：International Journal of Statistics and Probability
印刷版ISSN：1927-7032
电子版ISSN：1927-7040
出版年度：2019
卷号：8
期号：2
页码：90-98
DOI：10.5539/ijsp.v8n2p90
出版社：Canadian Center of Science and Education
摘要：This article derives the probability density function ψ(ξ;x,x') of the resulting speed ξ from the collision of two particles with speeds x and x' . This function had been left unsolved for about 150 years. Then uses two approaches to obtain the Maxwell speed distribution: (1) Numerical iteration: using the equation P_new(ξ) =∫_0^∞ ∫_0^∞ψ(ξ;x,x') ∙P_old(x) ∙P_old(x') dxdx' to get the new speed distribution from the old speed distribution. Also, after 9 iterations, the distribution converges to the Maxwell speed distribution. (2) Analytical integration: using the Maxwell speed distribution as the P_old(x) , and then getting P_new(ξ) from the above integration. The result of P_new(ξ) from analytical integration is proved to be exactly the Maxwell speed distribution.
关键词：Maxwell speed distribution; Maxwell-Boltzmann distribution; collision of particles; kinetic theory of
gases
